Apparatus and methods for improving the stability of RF power delivery to a plasma load

ABSTRACT

Methods for improving the stability of RF power delivery to a plasma load are disclosed. The method includes adding an RF resistor and/or a power attenuator at one of many specific locations in the RF power system to lower the impedance derivatives while keeping the matching circuit substantially in tune with the RF transmission line.

This application claims benefit of Provisional No. 60/362,745 filed Mar.8, 2002.

BACKGROUND OF THE INVENTION

The present invention relates to methods and apparatus for improving thestability of RF power delivery to a plasma load in a plasma processingsystem.

Plasma processing systems have been around for some time. Over theyears, plasma processing systems utilizing inductively coupled plasmasources, electron cyclotron resonance (ECR) sources, capacitive sources,and the like, have been introduced and employed to various degrees toprocess semiconductor substrates and glass panels.

During processing, multiple deposition and/or etching steps aretypically employed. During deposition, materials are deposited onto asubstrate surface (such as the surface of a glass panel or a wafer). Forexample, deposited layers comprising various forms of silicon, silicondioxide, silicon nitride, metals and the like may be formed on thesurface of the substrate. Conversely, etching may be employed toselectively remove materials from predefined areas on the substratesurface. For example, etched features such as vias, contacts, ortrenches may be formed in the layers of the substrate. Note that someetch processes may utilize chemistries and/or parameters thatsimultaneously etch and deposit films on the plasma-facing surfaces.

The plasma can be generated and/or sustained using a variety of plasmageneration methods, including inductively-coupled, ECR, microwave andcapacitively-coupled plasma methods. In an inductively-coupled plasmaprocessing chamber, for example, an inductive source is employed togenerate the plasma. To facilitate discussion, FIG. 1 illustrates aprior art inductive plasma processing chamber 100, which is configuredfor etching in this example. Plasma processing chamber 100 includes asubstantially cylindrical chamber wall portion 102 and an antenna orinductive coil 104 disposed above a dielectric window 106. Typically,antenna 104 is operatively coupled to a first radio frequency (RF) powersource 108, which may include an RF generator 110 and an RF matchnetwork 112 as shown. RF generator 110 may operate at a frequency of,for example, 4 MHz. Generally speaking, the RF signals from the RFgenerators may be sinusoidal, pulsed, or non-sinusoidal. Dielectricwindow 106 is typically formed of a high resistivity dielectricmaterial, such as high resistivity silicon carbide (SiC).

Within plasma processing chamber 100, a set of inlet gas ports (notshown) is typically provided to facilitate the introduction of gaseoussource materials, e.g., the etchant source gases, into the RF-inducedplasma region between dielectric window 106 and a substrate 114.Substrate 114 is introduced into chamber 100 and disposed on a chuck116. Chuck 116 generally acts as an electrode and is operatively coupledto a second RF power source 118, which may include an RF generator 120and an RF match network 122 as shown. RF generator 120 may operate at anRF frequency of, for example, 13.56 MHz. As mentioned, the RF signalfrom RF generator 120, like other RF signals from the RF generators, maybe sinusoidal, pulsed, or non-sinusoidal.

In order to create a plasma, a process source gas is input into chamber100 through the aforementioned set of inlet gas ports. Power is thensupplied to inductive coil 104 using RF power source 108 and to chuck116 using RF power source 118. The supplied RF energy from RF powersource 108 coupled through dielectric window 106 excites the processsource gas and a plasma 124 is generated thereby.

Chamber 100 may also be provided with different components, depending onthe specific manufacturer thereof and/or the requirements of aparticular process. For example, focus rings, plasma screens, magnets,pressure control rings, hot edge rings, various gas injector nozzles,probes, chamber liners, etc., may also be provided. To simplify theillustration, these well-known components are omitted from FIG. 1.

Generally speaking, it is critical to maintain tight control of the etchprocess in order to obtain a satisfactory etch result Thus, parameterssuch as the antenna RF voltage, antenna RF power, bias RF voltage, biasRF power, plasma density, the amount of contamination in the chamber,and the like, must be carefully controlled. Furthermore, it is importantto maintain a tight control of the etch process over as wide a processwindow as possible. In this regard, the stability of the RF powerdelivery to the plasma load is a particularly important issue. For agiven process recipe, it is crucial that the RF power delivery remainstable throughout the process to obtain a reliable process result.

This invention deals with methods and apparatus for improving thestability of the RF power delivery to the plasma in a plasma processingchamber as well as methods for quantifying parameters contributing tothe stability of the RF power delivery to the plasma at a givenparameter setting.

SUMMARY OF THE INVENTION

The invention relates, in one embodiment, to a method for configuring aplasma processing system. The plasma processing system is configured forprocessing semiconductor substrates. The method includes providing an RFpower arrangement, which includes an RF generator having an RF generatoroutput, a first RF transmission line coupled to receive RF current fromthe RF generator output during operation, the first RF transmission linehaving a characteristic impedance, a matching network having an inputimpedance substantially equal to the characteristic impedance of thefirst RF transmission line, the matching network being configured toreceive the RF current from the RF generator through the first RFtransmission line. The method includes coupling an RF power attenuatorin a current path between the RF generator and the matching network.

In another embodiment, the invention relates to a plasma processingsystem, which includes an RF generator having an RF generator output.There is included a first RF transmission line coupled to receive RFcurrent from the RF generator output, the first RF transmission linehaving a characteristic impedance. There is additionally included amatching network having an input impedance substantially equal to thecharacteristic impedance of the first RF transmission line, the matchingnetwork being configured to receive the RF current from the RF generatorthrough the first RF transmission line. There is further included an RFpower attenuator coupled in a current path between the RF generator andthe matching network.

In yet another embodiment, the invention relates to a plasma processingsystem for processing semiconductor substrates, which includes an RFgenerator having an RF generator output. There is included an RFtransmission line coupled to the RF generator output, the RFtransmission line having a characteristic impedance. There is furtherincluded a matching circuit coupled to the RF transmission line, thematching circuit having a first resistor and a matching network, thematching network having a plurality of impedance devices, wherein thefirst resistor is coupled to at least one terminal of one of theplurality of impedance device, and wherein an input impedance of thematching circuit is substantially equal to the characteristic impedanceof the RF transmission line.

In another embodiment, the invention relates to a plasma processingsystem, which includes an RF generator having an RF generator output.There is included a first RF transmission line coupled to receive RFcurrent from the RF generator output, the RF transmission line having acharacteristic impedance. There is additionally included a matchingnetwork having an input impedance substantially equal to thecharacteristic impedance of the RF transmission line, the matchingnetwork being configured to receive the RF current from the RF generatorthrough the RF transmission line, wherein both the input impedance ofthe matching network and the characteristic impedance of the RFtransmission line are substantially equal to a given value, the givenvalue being designed to be lower than 50Ω, the RF generator beingconfigured to deliver RF power into a load having the given value.

In yet another embodiment, the invention relates to a method forconfiguring a plasma processing system, the plasma processing systembeing configured for processing semiconductor substrates. The methodincludes providing an RF generator having an RF generator output. Themethod further includes configuring a first RF transmission line toreceive RF current from the RF generator output, the RF transmissionline having a characteristic impedance. The method additionally includesproviding a matching network having an input impedance substantiallyequal to the characteristic impedance of the RF transmission line, thematching network being configured to receive the RF current from the RFgenerator through the RF transmission line, wherein both the inputimpedance of the matching network and the characteristic impedance ofthe RF transmission line are substantially equal to a given value, thegiven value being designed to be lower than 50Ω, the RF generator beingconfigured to deliver RF power into a load having the given value.

These and other features of the present invention will be described inmore detail below in the detailed description of the invention and inconjunction with the following figures.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements and in which:

To facilitate discussion, FIG. 1 illustrates a prior art inductiveplasma processing chamber, which is configured for etching.

FIG. 2 is a block diagram illustrating the various electrical componentsof an exemplary RF power delivery arrangement involved in delivering RFpower to the plasma in an exemplary inductively coupled plasmaprocessing chamber.

FIG. 3 shows the source RF power system of FIG. 2 in greater detail.

FIG. 4A is an exemplary graph showing a process that experiences sourceRF power delivery instability at certain source RF delivered power setpoints.

FIG. 4B shows the observed optical emission of the plasma when source RFdelivered power becomes unstable.

The relationship between the matching network input impedance Z_(M), theload impedance Z_(T), and the generator output power P_(G) issymbolically illustrated in FIG. 5.

The interdependence of Z_(T) on P_(G) and of P_(G) On Z_(T) isillustrated schematically in FIG. 6, wherein P_(G) is a real number andZ_(T) is a complex number.

FIG. 7A models an RF generator having an RE voltage source with anoutput impedance Z_(OUT) and load impedance Z_(LOAD) in the case whereinchanges in the generator load impedance occurs at time scales fasterthan the generator feedback control bandwidth.

FIG. 7B shows exemplary RF power output contours as a function of loadimpedance Z_(LOAD) for a hypothetical RF generator when changes in theload impedance Z_(LOAD) occur for time scales faster than the generatorfeedback circuit response time.

FIGS. 8A, 8B, 8C, 8D, and 8E are exemplary circuit diagrams illustratingvarious embodiments of the present invention that utilize an extraresistance to reduce the impedance derivatives and to improve plasmastability.

FIG. 9 shows another embodiment wherein the impedance derivatives arereduced by intentionally an extra resistance such as R_(Y) to reduce theimpedance derivatives and to improve plasma stability.

FIG. 10A shows another embodiment where the impedance derivatives arereduced by using an RF power attenuator.

FIG. 10B shows the configuration of an exemplary Π-type RF powerattenuator.

FIG. 11 shows another embodiment of the invention wherein the impedancederivatives are reduced by designing the RF transmission line to have alower characteristic impedance R₀.

To further illustrate the non-obviousness of the invention, FIG. 12illustrates an implementation that merely dissipates power in theadditional resistor without conferring the benefit of improving RF powerdelivery stability.

FIGS. 13A and 13B show the effects that reducing the impedancederivative has on RF power delivery stability.

FIG. 14 shows the constituent impedances of an L-match network tofacilitate the calculation of $\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}.$

FIG. 15 shows the constituent impedances of a T-match network tofacilitate the calculation of $\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}.$

FIG. 16 illustrates, in accordance with one embodiment of the presentinvention, a technique for ascertaining the value of the addedresistance (e.g., R_(X) in FIG. 8 a) in order to make an unstable plasmamore stable.

FIG. 17A represents a plasma as a plot, with the real part of$P_{G}\frac{\partial Z_{T}}{\partial P_{G}}$being plotted along the x-axis, and the imaginary part of$P_{G}\frac{\partial Z_{T}}{\partial P_{G}}$being plotted against the y-axis.

FIG. 17B shows, for an exemplary RF generator, the RF generator stableoperating region.

FIG. 17C shows, for an exemplary RF generator, values of generatoroutput power times plasma impedance derivative that are always stableregardless of the phase of$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}.}$

FIG. 17D shows, for an exemplary RF generator, values of generatoroutput power times plasma impedance derivative that are stable but canbecome unstable for a change in phase of$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}.}$

FIG. 17E shows, for an exemplary RF generator, the plot of the regionwherein $P_{G}\frac{\partial Z_{T}}{\partial P_{G}}$results in unstable operation, regardless of the phase of$P_{G}\frac{\partial Z_{T}}{\partial P_{G}}$

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will now be described in detail with reference toa few preferred embodiments thereof as illustrated in the accompanyingdrawings. In the following description, numerous specific details areset forth in order to provide a thorough understanding of the presentinvention. It will be apparent, however, to one skilled in the art, thatthe present invention may be practiced without some or all of thesespecific details. In other instances, well known process steps and/orstructures have not been described in detail in order to notunnecessarily obscure the present invention.

In order to discuss the effects that derivatives of electrical loadimpedance with respect to delivered RF power exert on RF powerstability, a brief review of an exemplary RF power delivery arrangementmay be useful. FIG. 2 is a block diagram illustrating the variouselectrical components of an exemplary RF power delivery arrangementwhich is involved in delivering RF power to the plasma in an exemplaryinductively coupled plasma processing chamber. It should be kept in mindthat although an inductively coupled plasma processing system isarbitrarily chosen to facilitate discussion, the invention appliesequally well to capacitively coupled plasma processing systems as wellas to other plasma processing systems that generate and/or sustain theirplasmas using other methods.

In FIG. 2, there is shown a source RF power system 202 coupled to acontrolling computer 204 and a source RF antenna 206. Controllingcomputer 204 is a part of the feedback control loop that employsfeedback from sensors 208 and 210 and/or from a source RF generator 212to control source RF generator 212 and impedance matching network 214.Sensor 208 include sensors for monitoring parameters that reflect theperformance of source RF generator 212. Thus, parameters such as themagnitude and/or phase of the RF current and voltage, the forward RFpower from the source RF generator to the impedance matching network,the reflected RF power from the impedance matching network to the sourceRF generator, and the like may be measured by sensor 208. Theinformation obtained by sensor 208 is employed by controlling computer204 and source RF generator 212 to adjust the RF power delivery fromsource RF generator 212 during processing.

Sensor 210 include sensors for monitoring parameters that reflect theperformance of impedance matching network 214. Thus, parameters such asthe magnitude and/or phase of the RF current and voltage, the forward RFpower from the source RF generator to the impedance matching network,the reflected RF power from the impedance matching network to the sourceRF generator, and the like may be measured by sensor 210. Duringoperation, source RF generator generates RF power, which is delivered tosource RF antenna 206 via a source RF transmission line 216 andimpedance matching network 214 as shown.

In FIG. 2, there is also shown a bias RF power system 222 coupled tocontrolling computer 204 and a bias RF electrode 226. Controllingcomputer 204 performs an analogous role in bias RF power system 222.That is, controlling computer 204 is a part of the feedback control loopthat employs feedback from sensors 228 and 230 and/or from a bias RFgenerator 232 to control bias RF generator 232 and impedance matchingnetwork 234. Sensors 228 and 230 perform functions analogous to thoseperformed by sensors 208 and 210 in the source RF power system 202.During operation, bias RF generator 232 generates RF power, which isdelivered to bias RF electrode 226 via a bias RF transmission line 236and impedance matching network 234 as shown.

FIG. 3 shows the source RF power system 202 of FIG. 2 in greater detail,including labeling for various electrical parameters at various pointsin the system. In FIG. 2, the impedance matching network is arbitrarilychosen to be a T-type matching network to facilitate discussion. Itshould be noted, however, that the invention also applies with othermatching network types, such as L-type or Π-type matching networks.

With reference to FIG. 3, there is shown a plasma having a plasmaimpedance Z_(P), representing the complex impedance of the plasma.Z_(P)=R_(P)+jωL_(P) where R_(P) and L_(P) are the plasma resistance andinductance, respectively, j=√{square root over (−1)}, and ω=2πf (f isthe RF frequency, in Hz).

For this example of an inductive plasma source, the plasma can bemodeled as the secondary loop of a transformer for which the RF antennais the primary loop. In this model, the plasma impedance Z_(P) istransformed into an effective impedance Z_(S) in series with theantenna.

Z_(S)=R_(S)+jX_(S), with R_(S) and X_(S) (reactance) given by:$R_{S} = {{\left( \frac{\omega^{2}M^{2}R_{p}}{R_{p}^{2} + {\omega^{2}L_{p}^{2}}} \right)\quad X_{S}} = \left( \frac{{- \omega^{3}}M^{2}L_{p}}{R_{p}^{2} + {\omega^{2}L_{p}^{2}}} \right)}$where M is the mutual inductance between inductors L_(A) and L_(P).

(This derivation can be found, for example, in Albert Lamm,“Observations Of Standing Waves On An Inductive Plasma Cell Modeled As AUniform Transmission Line,” J. Vac. Sci. Technol. A15, 2615 (1997),incorporated herein by reference).

Source RF antenna inductance L_(A) (in henries) is attributable to thesource RF antenna 206 of FIG. 2.

X_(A)=ωL_(A) is the inductive reactance, in ohms, of the source RFantenna.

Impedance matching network 214 of FIG. 2, which is arbitrarily selectedas a T-type matching network in FIG. 3 for discussion purposes, isrepresented by three exemplary capacitors: C_(a), C_(b), C_(c), of whichC_(a) and C_(c) may be tunable. In FIG. 3, the impedance matchingnetwork is implemented by capacitors although inductors or a combinationof capacitors and inductors may well be employed. A terminatingcapacitor C_(d) is also shown in series with the source RF antennainductance L_(A).${X_{a} = \frac{- 1}{\omega\quad C_{a}}};\quad{X_{b} = \frac{- 1}{\omega\quad C_{b}}};\quad{X_{c} = \frac{- 1}{\omega\quad C_{c}}}$are the capacitive reactances, in ohms, of capacitors C_(a), C_(b) andC_(c). $X_{d} = \frac{- 1}{\omega\quad C_{d}}$is the capacitive reactance, in ohms, of terminating capacitor C_(d).

Z_(M) is the input impedance of the impedance matching network,including the effective series plasma impedance Z_(S), the source RFantenna inductance L_(A), the impedances of the matching networkcomponents C_(a), C_(b), and C_(c), and the impedance of any terminatingcapacitance C_(d). Z_(M) = R_(M) + jX_(M)$R_{M} = \frac{X_{b}^{2}R_{S}}{R_{S}^{2} + \left( {X_{b} + X_{3}} \right)^{2}}$$X_{M} = {\frac{{X_{b}R_{S}^{2}} + {X_{b}{X_{3}\left( {X_{b} + X_{3}} \right)}}}{R_{S}^{2} + \left( {X_{b} + X_{3}} \right)^{2}} + {X_{a}\quad{where}}}$X₃ = X_(c) + X_(S) + X_(A) + X_(d)where X₃=X_(c)+X_(S)+X_(A)+X_(d)

In normal operation of the impedance matching network, capacitors C_(a)and C_(c) are generally adjusted so that X_(M)=0 and R_(M)=R₀, where R₀is the characteristic resistance of the source RF transmission line.

The input impedance Z_(M) of the impedance matching network istransformed by the source RF transmission line into a transformed valueZ_(T) given by: $\begin{matrix}{Z_{T} = {R_{0}\frac{Z_{M} + {{jR}_{0}{\tan\left( {2\pi\quad{L/\lambda}} \right)}}}{R_{0} + {{jZ}_{M}{\tan\left( {2\pi\quad{L/\lambda}} \right)}}}}} & {{Equation}\quad 1}\end{matrix}$where R₀ is the characteristic resistance of the RF transmission line, Lis the length of the RF cable, and λ is the wavelength of the RF wave inthe transmission line (assuming lossless cable). (See, for example,Electronics Engineers' Handbook, Third Edition, D. Fink and D.Christiansen, editors, McGraw-Hill, N.Y., 1989, page 9-3)

In normal, tuned operation, Z_(M)=R₀ and Z_(T)=R₀.

P_(G) represents the generator output power in watts, whereas P_(P)represents the power actually delivered to the plasma. P_(G) is equal tothe sum of P_(P) plus any power reflected back to the generator ordissipated in the matching circuit elements.

As mentioned earlier, the stability of the RF power delivery is highlyimportant in achieving a satisfactory process result. FIG. 4A is anexemplary graph showing a process that experiences source RF powerdelivery instability at certain source RF delivered power set points. Inexemplary FIG. 4A, the process is stable when the source RF deliveredpower set point is above 370 watts. Below 370 watts, the source RF powerdelivered to the plasma is no longer stable and the reflected RF power(as measured by, for example, sensors 208 of FIG. 2) becomes high.

FIG. 4B shows the observed optical emission of the plasma when source RFdelivered power becomes unstable. As can be seen, the broadband opticalemission intensity fluctuates widely, with the amplitude swing exceeding25% during the instability period. As can be appreciated by thoseskilled in the art, such fluctuation severely degrades the processresult and needs to be rectified.

In the past, the RF power delivery instability problem is addressed bytrying out different RF generator/transmission cable length combinationsuntil stable RF power delivery is achieved for the chosen processrecipe. Having characterized an exemplary inductively coupled source RFpower system in electrical terms, the RF power instability problem forany RF power system may now be discussed in view of the characterizationdone with respect to FIGS. 2 and 3.

In general, the load impedance Z_(L) (as seen by the matching network)includes Z_(S) which depends on P_(P), the power delivered to theplasma. The matching network transforms the load impedance Z_(L) intothe matching network input impedance Z_(M). As a result, the matchingnetwork input impedance Z_(M) is a function of the power delivered tothe plasma P_(P), orZ_(M)=Z_(M)(P_(P))

When the matching network is tuned, Z_(M) is typically (50+0j) Ω.

RF generator systems typically contain an active feedback loop thatmaintains the generator forward (i.e., output) power or delivered power(i.e., forward power minus reflected power) equal to some pre-selectedvalue. For changes in load impedance Z_(T) (as seen by the generator)that occur on the time scales slow compared to the response time of thefeedback circuit, the generator forward (or delivered) power will remainconstant due to the operation of the feedback circuit.

However, the generator output power P_(G) does vary with changes in loadimpedance Z_(T) that occur on time scales comparable to or faster thanthe response time of the feedback circuit Thus, for time scalescomparable to or faster than the response time of the feedback circuit,the generator output power P_(G) is a function of the load impedanceZ_(T), orP_(G)=P_(G)(Z_(T))

As mentioned earlier, the load impedance Z_(L) (as seen by the matchingnetwork) depends on P_(P), the power delivered to the plasma. Forchanges in the plasma impedance Z_(S) that occur on a time scale slowerthan the response time of the impedance matching network, the matchingnetwork input impedance Z_(M)=R₀, and the matching network inputimpedance Z_(M) and the load impedance Z_(T) do not depend on the powerdelivered to the plasma P_(P) or the generator output power P_(G).

However, changes in the plasma impedance Z_(S) that occur on a timescale equal to or faster than the response time of the impedancematching network results in Z_(M)≠R₀ and the load impedance Z_(T) is afunction of the power delivered to the plasma P_(P), orZ_(T)=Z_(T)(P_(P)). If the relationship between P_(G) and P_(P) isknown, then the load impedance can be expressed as a function of P_(G)as follows:Z_(T)=Z_(T)(P_(G))

The relationship between the matching network input impedance Z_(M), theload impedance Z_(T), and the generator output power P_(G) issymbolically illustrated in FIG. 5.

It is believed that the RF power delivery instability depends on theloop gain of the feedback loop between the generator load impedanceZ_(T), and the generator output power P_(G). More specifically, theoverall gain of the loop of interdependence of the load impedance Z_(T)and the generator output power P_(G) contributes substantially to the RFpower delivery instability.

For small changes in the load impedance Z_(T) when the value of Z_(T) isaround the value of R₀, the dependence of Z_(T) on the generator outputpower P_(G) can be expressed as the derivative${\frac{\partial Z_{T}}{\partial P_{G}}❘_{Z_{T} = R_{O}}},$which is a complex number.

The dependence of the generator output power P_(G) on the load impedanceZ_(T) can be expressed as the gradient ∇P_(G)(Z_(T)), which is also acomplex number.

The interdependence of Z_(T) on P_(G) and of P_(G) on Z_(T) isillustrated schematically in FIG. 6, wherein P_(G) is a real number andZ_(T) is a complex number. The tendency for the RF power delivery systemto be stable or unstable depends on$\frac{\partial Z_{T}}{\partial P_{G}} \cdot {\nabla P_{G}}$where • is a dot product.

Furthermore, it is hypothesized that when the value of$\frac{\partial Z_{T}}{\partial P_{G}} \cdot {\nabla P_{G}}$is reduced, the RF power delivery to the plasma tends to be more stable.In accordance with one aspect of the present invention, the reduction in$\frac{\partial Z_{T}}{\partial P_{G}}$is achieved by techniques that happen to “waste” a portion of the RFgenerator output power P_(G), thereby requiring an increase in P_(G) inorder to maintain the same power P_(P) delivered to the plasma. However,it is necessary to ascertain that an increase in the RF generator outputpower P_(G) does not cause a detrimental change in ∇P_(G)(Z_(T)), whichmay negate the benefit of reducing$\frac{\partial Z_{T}}{\partial P_{G}}.$FIGS. 7A and 7B show that this is not the case.

When changes in the generator load impedance occurs at time scalesfaster than the generator feedback control bandwidth, the RF generatormay be modeled as an RF voltage source with an output impedance Z_(OUT)and load impedance Z_(LOAD).

This model is shown in FIG. 7A.

For such a model, it is observed that there exist normalized poweroutput contours, which are determined by the generator characteristicsand have a general shape G(Z_(LOAD)), which is independent of outputpower. FIG. 7B shows exemplary RF power output contours as a function ofload impedance Z_(LOAD) for a hypothetical RF generator when changes inthe load impedance Z_(LOAD) occur for time scales faster than thegenerator feedback circuit response time. In FIG. 7B, the generatoroutput impedance Z_(OUT) is arbitrarily chosen to be (5+0j) Ω, and theRF generator has a nominal output power of 100% into a 50Ω load. Theoutput power is 120% into a 40 Ω load and 86% into a 60Ω load. Thehypothetical generator can reasonably model a typical RF generatoralthough in reality the imaginary part of a typical generator's outputimpedance is not at zero but the real part of a typical generator'soutput impedance is typically low, on the order of the few ohms, inorder to maintain a high level of efficiency. Including a non-zeroimaginary part will change the shape of the power contours somewhat butdoes not change the premise that these power contours exist.

It should be noted at this point that for changes in load impedanceZ_(LOAD) that occur much slower than the generator feedback circuitresponse time, the generator feedback circuit tends to keep the outputpower approximately constant. Further, for changes in load impedanceZ_(LOAD) that occur on about the same time scale as the generatorfeedback circuit response time, the output power depends on the detailsof the feedback circuit, and the power contours may have morecomplicated shapes than those show in FIG. 7B.

In the case where changes in the load impedance Z_(LOAD) occur fasterthan the generator feedback circuit response time, the RF power contoursappear to be determined by the specific characteristics of individualgenerators and have a general shape G(Z_(LOAD)), which is independent ofoutput power. Assuming that the generator output power is P_(0(R) ₀) forload impedance R₀, then the generator output power for any other loadimpedance Z_(Load) is given by:

 P _(G)(Z _(Load))=P _(G)(R ₀)*G(Z _(LOAD)), and ∇P _(G) =P _(G) ∇G

Under this assumption, the stability of the RF power delivery may bedetermined by $\begin{matrix}{{\frac{\partial Z_{T}}{\partial P_{G}} \cdot {\nabla P_{G}}} = {{P_{G}{\frac{\partial Z_{T}}{\partial P_{G}} \cdot {\nabla G}}} = {P_{G}\frac{\mathbb{d}P_{P}}{\mathbb{d}P_{G}}{\frac{\partial Z_{T}}{\partial P_{P}} \cdot {\nabla G}}}}} & {{Equation}\quad 2}\end{matrix}$where the term ∇G depends on the generator characteristics and isgenerally independent of the generator output power P_(G). The term$\frac{\partial Z_{T}}{\partial_{P}}$depends on the characteristics of the plasma (defined by gascomposition, pressure, delivered power P_(P), etc.), the impedancematching network, and the length of the RF transmission line. As anaside, it should be noted that the length of the RF transmission lineaffects the direction, but not the magnitude of the impedance derivative(See Appendix A).

It is observed that, for a given RF generator, plasmas (defined by gascomposition, pressure, delivered power P_(P), etc.) that have low valuesof $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$are stable over a wider range of lengths of RF transmission line thanare plasmas with high values of$P_{G}{{\frac{\partial Z_{T}}{\partial P_{G}}}.}$

From these observations and deductions, it is believed that RF powerdelivery stability to the plasma load may be improved by at least twomechanisms:

-   -   1) changing the impedance matching network to reduce the        magnitude of ${P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}},$        evaluated at Z_(T)=R₀. This improvement can be performed with        any existing or future RF generator; and    -   2) changing the generator output characteristics to reduce the        magnitude of        ${{\nabla G}} = {\frac{1}{P_{G}}{{{\nabla P_{G}}}.}}$

In one embodiment, the value of$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$may be reduced by intentionally introducing additional resistance inseries with the input of the matching network and/or coupled to one ofthe terminals of the impedance devices of the matching network such thatthe current that flows into the input terminal also flows through theadditional resistance (for example in the cases shown in FIGS. 8B and8D, which are discussed later herein).

As the term is employed herein, the matching network has an inputterminal and an output terminal. The input terminal of the matchingnetwork represents the terminal disposed toward the RF generator, whilethe output terminal of the matching network represents the terminaldisposed toward the load (e.g., the RF antenna).

The matching circuit that comprises the existing matching network andthe additional resistor remains tuned, i.e., not mistuned, for thisembodiment. As the term is employed therein, the matching circuit isconsidered tuned or in tune when its input impedance substantiallyequals the characteristic impedance of the RF transmission line, i.e.,these two values are considered equal within industry-accepted tolerancesince in the real world, absolutely exact matching is not alwayspossible or practical.

FIG. 8A is an exemplary circuit diagram illustrating this embodiment. InFIG. 8A, a power resistor R_(X) is inserted in series with the input ofT-match network 802. For ease of discussion, assume that R_(X) has thevalue of 25Ω. The addition of a high-power 25Ω RF resistor in scrieswith input of matching network 802 allows the modified matching circuit,which includes R_(X), to stay tuned to 50Ω (i.e, Z_(M2)=50+0j Ω) eventhough the matching network 802 itself now tunes to only 25Ω (i.e,Z_(M1)=25+0j Ω). Tuning the matching network 802 to Z_(M1)=25Ωeffectively reduces the value of R_(M) by half, and according toequation C6 of Appendix C, reduces the impedance derivative$\frac{\partial Z_{M}}{\partial Z_{S}}$by half.

It can be seen that the matching network transforms Z_(S) intoZ_(M1)=(25+0j) Ω, and in the process magnifies the impedance derivativesby the ratio${\frac{\mathbb{d}Z_{M1}}{\mathbb{d}Z_{S}}} = {\frac{25\Omega}{R_{S}}.}$But since Z_(M2)=25Ω+Z_(M1) (the 25Ω part does not depend on the powerdelivered to the plasma P_(P)),${{\frac{\partial Z_{M2}}{\partial P_{P}}} = {{\frac{\partial Z_{M1}}{\partial P_{P}}} = {\frac{25\Omega}{R_{S}}*{\frac{\partial Z_{S}}{\partial P_{P}}}}}},$which is only half as large as the value$\frac{50\Omega}{R_{S}}*{\frac{\partial Z_{S}}{\partial P_{P}}}$of the unmodified matching network.

The total loop gain, believed responsible for the instability, is givenby${P_{G}\frac{\partial Z_{T}}{\partial P_{G}}*{\nabla G}} = {P_{G}\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}}\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}\frac{\mathbb{d}P_{P}}{\mathbb{d}P_{G}}\frac{\partial Z_{S}}{\partial P_{P}}*{\nabla G}}$

In this example for which R_(X)=25Ω, P_(G) is twice as big as for${R_{X} = 0},\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}}$has magnitude=1, $\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}$has magnitude half as big as for R_(X)=0,${\frac{\mathbb{d}P_{P}}{\mathbb{d}P_{G}} = 0.5},$and $\frac{\partial Z_{S}}{\partial P_{P}}$and ∇G are the same, so the net effect is to reduce the magnitude of theloop gain by a factor of 2x.

Note that in this case, the matching circuit 806 that comprises matchingnetwork 802 and resistor R_(X) remains in tune to the characteristicimpedance of the RF transmission line. No RF power will be reflectedfrom the matching network. Approximately half of the generator's powerwill be dissipated in the 25Ω resistor R_(X) so the generator outputP_(G) should be twice as large to get the same power P_(P) delivered tothe plasma. Further, the resistor R_(X) needs to handle a large amountof power dissipation and should be selected and/or designedappropriately. For example, in some cases, liquid-cooled high powerresistive arrangements may be employed.

Note that in FIG. 8A, although the resistor is shown disposed to theleft of the matching network's variable capacitor C_(a) along thecurrent path that flows through variable capacitor C_(a) (i.e., theresistor is disposed between the RF transmission line and the inputterminal of the matching network), the resistor may also be disposedbetween variable capacitor C_(a) and a terminal 804 (the T-junction inFIG. 8A) of the matching network. In another embodiment, both thevariable capacitor C_(b) of the match network 802 and the terminatingcapacitor C_(d) are coupled together prior to being coupled to ground.This is shown in FIG. 8B. In this case, the resistor R_(X) may bedisposed along the current path that flows through the equivalentimpedance that is formed by capacitors C_(b) and C_(d) in parallel andground.

Further, in FIG. 8A, a T-match network is employed as an examplealthough it should be noted that analogous results would also beobtained for L-match and Π-match networks (see Appendices B and Cherein). In an L-match, the additional resistance may be provided, forexample, between the RF transmission line and the input terminal of theL-match, such as shown in FIG. 8C, or may be provided in series betweenthe equivalent impedance that is formed by impedance elements Z_(L1) andZ_(L2) in parallel and ground (as shown in FIG. 8D). In either case(e.g., FIG. 8C or FIG. 8D), the additional resistance is considered tobe in series with the input of the matching network.

In the L-match case of FIG. 8C (and analogously in FIG. 8D), theadditional resistance may alternatively be provided at locations 840 or842. Although the additional resistance is not considered to be inseries with the input of the matching network when disposed at position840 or 842, the provision of the additional resistance at theselocations also reduces the impedance derivatives and results in improvedplasma stability.

In the Π-match case such as that shown in FIG. 8E, the additionalresistance may be provided, for example, between input terminal 862 andthe line-side T-junction 860 of the Π-match at the location indicated byreference number 850. The additional resistance may alternately beprovided, for example, between the line-side T-junction 860 of theΠ-match and capacitor Z_(Π2) at the location indicated by referencenumber 858. The additional resistance may alternately be provided, forexample, between the electrode-side T-junction 864 of the Π-match andcapacitor Z_(Π3) at the location indicated by reference number 856. Theadditional resistance may alternately be coupled, for example, betweenthe line-side T-junction 860 of the Π-match and electrode-sideT-junction 864 of the Π-match capacitor Z_(Π2) at the location indicatedby reference number 852. The point is that the additional resistance, inconjunction with a matching network that is tuned to a lower value,would present in combination a matching circuit having an inputimpedance substantially equal to the characteristic impedance of the RFtransmission line.

When the additional resistance is implemented at positions 852, 856, or858, for example, the value of the additional resistance required toreduce the impedance derivatives by a certain percentage point maydiffer from the value of the additional resistance R_(X) required toreduce the impedance derivatives by the same percentage point when thatadditional resistance R_(X) is implemented in series with the inputimpedance of the matching network, e.g., at location 850.

Furthermore, the variable impedance elements of the matching network(T-match 802, or L-match, or Π-match) may be implemented using inductorsor a combination of inductors/capacitors instead. It is expected thatthe resistor R_(X) can be positioned analogously in the manner discussedabove in an RF power system utilizing inductors or a combination ofinductors/capacitors for the matching network's impedance elements.

Furthermore, although 25Ω is chosen to be the value of R_(X) tofacilitate discussion, R_(X) can have any desired value. In oneembodiment, the resistance value of the additional resistor is between10% and 90% of the total input impedance of the matching circuit (e.g.,806 of FIG. 8A). In another embodiment, the resistance value of theresistor is between 20% and 80% of the total input impedance of thematching circuit. Thus, the resistance value of the additional resistorR_(X), while larger than the typical inherent resistance along the samecurrent path in existing RF power systems, may be varied so as to reducepower “waste” while finishing the desired plasma stabilizing effect fora given process.

Furthermore, the additional resistor R_(X) may even be a variable or aswitched resistor. That is, the additional resistor R_(X) may be madevariable in resistance to account for different processes or switchedoff if not needed. For example, some processes may be stable withoutrequiring the use of the resistor R_(X). In this case, the resistorR_(X) may be turned off, and may be turned on only when another processrecipe requires the extra plasma stabilizing effects thereof. Since alarger resistor “wastes” a larger amount of power, it may be preferableto employ a variable resistor so that an appropriately sized resistorvalue that is sufficient to provide the desired plasma stabilizingeffect for a given process can be utilized.

One should note that resistor R_(X) may not necessarily be a discreteresistor. For example, it may be possible to intentionally employ a lowconductance (e.g., higher resistance) material for components such asfixed inductors (such as those employed in some matching networks),connectors such as the conductor or strap between the RF transmissionline and the input of the matching network, or the conductor or strapbetween an element of the matching network and a terminal therein alongthe relevant current path (e.g., between capacitor C_(a) and terminal804 in the example of FIG. 8A). The low conductance material representsmaterials whose resistance is higher than those associated with typicalconductors (such as copper, silver-plated copper, aluminum, or theiralloys) and may include, for example, 316 stainless steel, nichrome,chromel, graphite, SiC, or the like. The point is resistor R_(X) wouldtypically be larger than the inherent resistance of typical conductorsand may be implemented in various ways.

FIG. 9 shows another alternative embodiment wherein the impedancederivatives are reduced by intentionally adding resistance R_(Y) inseries with the effective series plasma impedance Z_(S). With referenceto equation C6 of Appendix C, the implementation of the exemplarycircuit of FIG. 9 essentially replaces the impedance Z_(S)=X_(S)+R_(S)with the new impedance Z_(S)+R_(Y)=X_(S)+R_(S)+R_(Y).

Accordingly, the modified equation C6 for Appendix C is:${\frac{\mathbb{d}Z_{M}}{\mathbb{d}\left( {Z_{S} + R_{Y}} \right)}} = \frac{R_{M}}{R_{S} + R_{Y}}$

In this case, since R_(Y) is a fixed-value resistor, its value does notdepend on power delivered to the plasma P_(P), and${\frac{\mathbb{d}Z_{M}}{\mathbb{d}\left( {Z_{S} + R_{Y}} \right)}} = {\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}}$

With the addition of resistor R_(Y), the magnitude$\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}$of the variation of the match network input impedance Z_(M) with respectto the series plasma impedance Z_(S) is lower by a factor of$\frac{R_{S}}{R_{S} + R_{Y}}$than when R_(Y) is not present.

In this example, a fraction $\frac{R_{Y}}{R_{S} + R_{Y}}$of the generator output power P_(G) is dissipated in the resistor R_(Y),so the generator output power must be increased by the factor$\frac{R_{S} + R_{Y}}{R_{S}}$in order for the power P_(P) delivered to the plasma to remain the same.

The total loop gain, believed responsible for the instability, is givenby${P_{G}{\frac{\partial Z_{T}}{\partial P_{G}} \cdot {\nabla G}}} = {P_{G}\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}}\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}\frac{\mathbb{d}P_{P}}{\mathbb{d}P_{G}}{\frac{\partial Z_{S}}{\partial P_{P}} \cdot {{\nabla G}.}}}$

Adding resistor R_(Y) requires that P_(G) increase by a factor of$\frac{R_{S} + R_{Y}}{R_{S}}$relative to the case with no added resistor R_(Y).$\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}}$has magnitude=1, $\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}$has magnitude that is smaller by the factor$\frac{R_{S}}{R_{S} + R_{Y}},\frac{\mathbb{d}P_{P}}{\mathbb{d}P_{G}}$is smaller by$\frac{R_{S}}{R_{S} + R_{Y}},\quad{{and}\quad\frac{\partial Z_{S}}{\partial P_{P}}}$and ∇G are the same, so the net effect is to reduce the magnitude of theloop gain by a factor of $\frac{R_{S}}{R_{S} + R_{Y}}.$

Note that the matching circuit that comprises the matching network 902and the additional resistor R_(Y) is still preferably tuned to thecharacteristic impedance of the RF transmission line, e.g., 50Ω. In thecase where an existing matching circuit is retrofitted by adding theadditional resistor R_(Y), for example, the impedance elements of thematching network may be tuned, after the additional resistor R_(Y) isadded, to tune the input impedance of the matching circuit to besubstantially equal to the characteristic impedance of the RFtransmission line.

If R_(S)=R_(Y) in our example, the magnitude of loop gain of theinstability is only half as large as the case when R_(Y) is not present.For the example of R_(Y)=R_(S), approximately half of the generator'spower will be dissipated in the resistor R_(Y) so the generator outputP_(G) should be at least twice as large to get the same power P_(P)delivered to the plasma. As in the example of FIG. 8A, the resistorR_(Y) needs to handle a large amount of power dissipation and should beselected accordingly. Further, R_(Y)is equal to R_(S) in the case ofFIG. 9, which may be substantially lower than 25Ω. One should also notethat the voltage across the LC resonance circuit formed by capacitorsC_(b), C_(c), and L_(A) of FIG. 9 may be high. These factors need to betaken into consideration when selecting the resistor R_(Y).

Note that in FIG. 9, although the resistor R_(Y) is shown disposed inbetween the matching network's variable capacitor C_(c) along thecurrent path that flows through the inductive coil (represented bysource RF antenna inductance L_(A)), the resistor R_(Y) may be disposedat other locations along the current loop. For example, the resistorR_(Y)may be disposed at any of alternate locations 910, 914, 916, 918,920, or 922 in FIG. 9.

Further, in FIG. 9, a T-match network is employed as an example althoughit should be noted that analogous results would also be obtained forL-match and Π-match networks (see Appendices B and C herein). In theL-match case, the capacitors C_(c) and C_(b) of FIG. 9 may be thought ofas the two capacitors of the L-match (with capacitor C_(a) being absentfrom the figure and the capacitor C_(b) being variable). In this case,the resistor R_(Y) may be coupled, for example, at the same locationsdiscussed in connection with the T-match case. The Π-match case isanalogous. Furthermore, the impedance elements of the matching network(T-match, or L-match, or Π-match) may be implemented instead usinginductors. It is expected that the resistor R_(Y) can be positionedanalogously in the manner discussed above in an RF power systemutilizing inductors for the matching network's impedance elements.

It should also be noted that although R_(Y) is chosen to have the valueof RS (i.e., the series equivalent plasma load resistance) to simplifythe discussion, R_(Y) can have any desired value (which of coursechanges the amount of power dissipated thereby as well as the degree ofstability improvement). In one embodiment, the resistance value of theadditional resistor is between 10% and 90% of the resistanceR_(S)+R_(Y). In another embodiment, the resistance value of the resistoris between 20% and 80% of the resistance R_(S)+R_(Y). Thus, theresistance value of the additional resistor R_(Y), while larger than thetypical inherent resistance along the same current path in existing RFpower system, may be varied so as to reduce power “waste” whilefurnishing the desired plasma stabilizing quality for a given process.

Furthermore, the additional resistor R_(Y) may even be a variable or aswitched resistor. That is, the additional resistor R_(Y) may be madevariable in resistance to account for different processes or switchedoff if not needed. For example, some processes may be stable withoutrequiring the use of the resistor R_(Y). In this case, the resistorR_(Y) may be turned off, and may be turned on only when another processrecipe requires the extra plasma stabilizing effects thereof. Since alarger resistor “wastes” a larger amount of power, it may be preferableto employ a variable resistor so that an appropriately sized resistorvalue that is sufficient to provide the desired plasma stabilizingeffect for a given process can be utilized.

One should note that resistor R_(Y) may not necessarily be a discreteresistor. For example, it may be possible to intentionally employ a lowconductance material for components such as fixed inductors (such asthose employed in some matching networks), connectors such as theconductor or strap between an element of the matching network and aterminal therein along the relevant current path (e.g., along thecurrent loop through variable capacitors C_(b) and C_(c), Z_(S), L_(A),and inductor C_(d)), or connectors between components along thatrelevant current path. The low conductance material represents materialswhose resistance is higher than those associated with typical RFconductors (such as copper, silver-plated copper, aluminum, or theiralloys) and may include, for example, 316 stainless steel, nichrome,chromel, graphite, SiC, or the like. The point is resistor R_(Y) wouldtypically be larger than the inherent resistance of typical conductorsand may be implemented in various ways.

FIG. 10A shows another embodiment where the impedance derivatives arereduced by using an RF power attenuator. In FIG. 10A, the attenuatorconsists of three resistors arranged in a T-network although it shouldbe noted that the same result would also be obtained for any of a numberof different attenuator configurations, including a Π-network (FIG. 10B), an L-network, a bridged-T network, etc.

In FIG. 10A, the RF power attenuator 1002 and the RF transmission line1004 are inserted in series between the RF transmission line 1006 andthe matching network 1008 as shown. Note that in the example of FIG.10A, matching network 1008 is still tuned to 50Ω. There is a loadimpedance at the output of the RF generator 1010 of 50Ω. RF powerattenuator 1002 transforms the load impedance at the RF generator outputto 50Ω. In other words, as far as impedance is concerned, RF powerattenuator 1002 has essentially no effect. However, RF power attenuator1002 does have an effect on the impedance change by magnifying themagnitude of the impedance change at one end by some ratio prior tooutputting the impedance at the other end.

The values of resistors R₁, R₂, and R₃ may be modified as necessary toobtain the desired power attenuation in response to a change inimpedance. If R₁=R₃=8.55Ω and R₂=141.9Ω, then the RF power attenuatortransmits 50% of power and dissipates 50% of power.

However, the attenuator reduces the magnitude of$\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}}$to 0.5, as will be shown below. With reference to FIG. 10A, Z_(M) is theinput impedance of the matching network, Z₄ is the impedance of thematching network as transformed by RF transmission line 1004, Z₅ is theinput impedance of the attenuator, and Z_(T) is the input impedance ofthe attenuator as transformed by RF transmission line 1006. Themagnitudes of${\frac{\mathbb{d}Z_{4}}{\mathbb{d}Z_{M}}}\quad{and}\quad{\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{5}}}$are equal to 1.0 as shown in Appendix A. Attenuator 1002 has inputimpedance Z₅ given by:$Z_{5} = {{R_{1} + \frac{R_{2}\left( {R_{3} + Z_{4}} \right)}{R_{2} + R_{3} + Z_{4}}} = {R_{1} + {\left\lbrack {R_{2}\left( {R_{3} + Z_{4}} \right)} \right\rbrack\left\lbrack {R_{2} + R_{3} + Z_{4}} \right\rbrack}^{- 1}}}$

For Z₄=50Ω and the values of R₁, R₂, and R₃ given above, Z₅=50Ω.

The equation for Z₅ can be differentiated to give the variation of Z₅with respect to changes in Z₄: $\begin{matrix}{\frac{\mathbb{d}Z_{5}}{\mathbb{d}Z_{4}} = {R_{2}\left\lbrack {\left( {R_{2} + R_{3} + Z_{4}} \right)^{- 1} - {\left( {R_{3} + Z_{4}} \right)\left( {R_{2} + R_{3} + Z_{4}} \right)^{- 2}}} \right\rbrack}} \\{= \frac{R_{2}^{2}}{\left( {R_{2} + R_{3} + Z_{4}} \right)^{2}}}\end{matrix}$

Evaluated at Z₄=50Ω;${\frac{\mathbb{d}Z_{5}}{\mathbb{d}Z_{4}}}_{Z_{4} = R_{0}} = {\frac{\left( {141.9\Omega} \right)^{2}}{\left( {{141.9\Omega} + {8.55\Omega} + {50\Omega}} \right)^{2}} = \frac{1}{2}}$

As such, the load impedance derivative as seen by the generator isreduced and plasma stability is improved.

Note that in the case of FIG. 10A, the matching network is in tune,i.e., not mistuned. In the example of FIG. 10A, approximately half ofthe generator's power will be dissipated in the RF power attenuator sothe generator output P_(G) should be at twice as large to get the samepower P_(P) delivered to the plasma. It should be noted that although aT-type attenuator arrangement is employed to discuss the implementationof FIG. 10A, other types of attenuator may well be employed. Forexample, 50% attenuation can also be achieved with a Π-type RF powerattenuator with R1=R3=292.4Ω; R2=17.6Ω. FIG. 10B shows the configurationof such a Π-type RF power attenuator. In any RF power attenuatorconfiguration, the values of the constituent resistors may be modifiedas necessary to obtain the desired power attenuation in response to achange in impedance.

The total loop gain, believed responsible for the instability, is givenby${P_{G}{\frac{\partial Z_{T}}{\partial P_{G}} \cdot {\nabla G}}} = {P_{G}\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{5}}\frac{\mathbb{d}Z_{5}}{\mathbb{d}Z_{4}}\frac{\mathbb{d}Z_{4}}{\mathbb{d}Z_{M}}\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}\frac{\mathbb{d}P_{P}}{\mathbb{d}P_{G}}{\frac{\partial Z_{S}}{\partial P_{P}} \cdot {\nabla G}}}$

In this example for which the attenuator dissipates ½ of the RF power,P_(G) must be twice as large in order for the power delivered to theplasma to be the same as without the attenuator.$\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{5}}\quad{and}\quad\frac{\mathbb{d}Z_{4}}{\mathbb{d}Z_{M}}$have magnitude=1, $\frac{\mathbb{d}Z_{5}}{\mathbb{d}Z_{4}}$has magnitude=0.5,${\frac{\mathbb{d}P_{P}}{\mathbb{d}P_{G}} = 0.5},\quad{{and}\quad\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}},\frac{\partial Z_{S}}{\partial P_{P}}$and ∇G are the same, so the net effect is to reduce the magnitude of theloop gain by a factor of 2x.

As in the case with FIGS. 8A and 9, the matching network therein mayhave other configurations (e.g., L-match, Π-match, transformer, etc.).Additionally, the impedance devices in the matching network may beimplemented using inductors instead, or using a combination of inductorsand capacitors.

Note that although FIG. 10A shows both RF transmission lines 1004 and1006, it is not absolutely necessary to have both RF transmission lines.For example, the RF power system of FIG. 10A may be implemented withonly RF transmission line 1004, or with only RF transmission line 1006.It is the combined length of 1004 and 1006 that determines the phase ofthe impedance derivatives as seen by the RF generator, and this combinedlength may be implemented by one or multiple RF transmission lines.

FIG. 11 shows another embodiment wherein the impedance derivatives arereduced by designing the RF transmission line to have a lowercharacteristic impedance R₀. In the example of FIG. 11, the RFtransmission line 1102 has a characteristic impedance R₀ of 25Ω insteadof the widely accepted 50Ω. For example, two 50Ω RF lines in parallelmay be employed to provide an RF transmission line having a acharacteristic impedance R₀ of 25Ω. In that case, the impedance matchingnetwork 1104 is tuned to a nominal value of 25Ω instead of the widelyaccepted 50Ω, and RF generator 1106 is designed to operate with a 25Ωload instead of the widely accepted 50Ω.

The matching network transforms Z_(S) into Z_(M)=25Ω, and in the processmagnifies the impedance derivative with respect to plasma deliveredpower P_(P) by $\frac{25\Omega}{R_{S}}.$The magnitude of $\frac{\mathbb{d}Z_{M}}{\mathbb{d}P_{P}}$is therefore only one-half as large as it would have been for Z_(M)=50Ω.

Note that in this case, the matching network is again in tune, i.e., notmistuned.

Unlike the situation of FIGS. 8A-8E, 9, and 10A-10B, however, a portionof the generator power is not dissipated in the matching circuit inorder to achieve improved stability. Furthermore, although 25Ω is chosento be the value of the characteristic impedance of the RF transmissionline to facilitate discussion, the characteristic impedance of the RFtransmission line R₀ can be reduced by any desired value (which ofcourse changes the value by which the impedance derivatives arereduced).

It is important to realize that it is the reduction in impedancederivative magnitude, not the reduction in power delivery efficiency perse, that improves RF power delivery stability. This point is not obviousand needs to be emphasized. This point is proven by the implementationof FIG. 11 in which it is not necessary to dissipate power away in orderto improve RF power delivery stability. To farther illustrate thenon-obviousness of the invention, FIG. 12 illustrates an implementationthat merely dissipates power in the additional resistor withoutconferring the benefit of improving RF power delivery stability. In FIG.12, an added resistor R_(Z) is added in series between the RF generator1202 and the RF transmission line 1204, which has the characteristicimpedance of 50Ω in this example.

The added resistor R_(Z) is given a value of also 50Ω to simplify thediscussion. The proof of no change in impedance derivative in spite ofthe reduction in power delivery is show below.${\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}}_{Z_{M} = R_{O}} = \frac{R_{O}}{R_{S}}$${\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}}} = 1$${\frac{\mathbb{d}Z_{6}}{\mathbb{d}Z_{T}}} = 1$

Thus,${{\frac{\mathbb{d}Z_{6}}{\mathbb{d}Z_{T}}} = \frac{R_{O}}{R_{S}}},$which is no change.

In other words, for the additional resistor R_(Z)=50Ω, half of thegenerator output power P_(G) is dissipated without change in${\frac{\mathbb{d}Z_{6}}{\mathbb{d}Z_{P}}}.$In the implementation of FIG. 12, there is a mismatch between thegenerator 1202 (designed for a 50Ω load) and the total load impedance,which is ˜100Ω, for R_(Z)=50Ω. One should note that in the case of FIG.12, RF power delivery stability can still be affected as the degree ofmismatch changes responsive to changes in the plasma impedance.Likewise, RF power delivery stability can also be affected when the RFgenerator runs into a different load, which changes the value at which∇G is evaluated.

FIGS. 13A and 13B show the effects that reducing the impedancederivative has on RF power delivery stability. With respect to FIG. 13A,there are shown two experimentally determined regions of instability1302 and 1304 for various combinations of plasma power (P_(P)) and RFcable length. In FIG. 13, the impedance derivative is reduced byemploying an RF power attenuator (as shown in FIG. 10), and the regionof instability 1306 of FIG. 13B is substantially smaller than those inFIG. 13A.

It is the case that every plasma process has some value of$P_{G}\quad{\frac{\partial Z_{T}}{\partial P_{G}}.}$This is a complex number with magnitude$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$and phase$\theta = {{\arg\left( \frac{\partial Z_{T}}{\partial P_{G}} \right)}.}$To improve plasma stability, the invention involves, in one embodiment,ascertaining the resistance value that can be added to the existing RFpower system in order to change the value of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$for an unstable plasma to be substantially identical and/or to approachmore closely to that for a stable plasma.

FIG. 16 illustrates, in accordance with one embodiment of the presentinvention, a technique for ascertaining the value of the addedresistance (e.g., R_(X) in FIG. 8 a) in order to make an unstable plasmamore stable. As a starting point, the two values of${P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}},$one for an unstable plasma and one for a stable plasma, are firstascertained (step 1602 and step 1604).

The value of $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$for the stable plasma can be a measured value, or it can be a valuechosen from within a range of values known to correspond to stableplasmas. The inventors believe that the value of$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$for the stable plasma can be obtained for any suitable process,employing any gas at any suitable parameter settings. Once the targetvalue $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$for one or more stable plasmas is obtained a plasma processing system,the value $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$for the process of interest can be reduced to the target value found,thereby resulting in a stable plasma for the process of interest.

The value of $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$for the unstable plasma can be a measured value, or an extrapolatedvalue, e.g., in cases where measurements may be difficult for unstableplasmas. For example, measurements of$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$may be made at parameter settings where the plasmas are known to bestable, and these measurements may thereafter be extrapolated to obtainextrapolated values for $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$at the parameter settings of interest.

The generator output power, P_(G), is the known output power of thegenerator. In one embodiment, the value of$\frac{\partial Z_{T}}{\partial P_{G}}$is measured by tuning the matching network with the generator outputpower at its nominal value. Once the matching network is so tuned, thematching network tuning element values are held fixed, and the generatoroutput power P_(G) is then varied.

Using an appropriate sensor, such as sensor 208 in FIG. 2, loadimpedance Z_(T) as a function of P_(G) may then be measured, and henceobtaining $\frac{\partial Z_{T}}{\partial P_{G}}.$In another embodiment, the value of$\frac{\partial Z_{T}}{\partial P_{G}}$is measured by tuning the matching network with generator output powerat its nominal value. Once the matching network is so tuned, thematching network tuning element values are held fixed, and the generatoroutput power P_(G) is then varied. Using an appropriate sensor, such assensor 210 in FIG. 2, the input impedance Z_(M) of the impedancematching network is then measured, and hence obtaining$\frac{\partial Z_{M}}{\partial P_{G}}.$Since dZ_(T) and dZ_(M) are related according to Equation A4, EquationA4 may be employed to transform $\frac{\partial Z_{M}}{\partial P_{G}}$into $\frac{\partial Z_{T}}{\partial P_{G}}.$

Once values of $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$have been determined for the unstable and target stable plasmas, thematching network tuned input impedance Z_(M) for the unstable plasma maybe reduced (step 1606) by the ratio of$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$for the unstable plasma to$P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$for the stable plasma (see equations A6 or B5).

As mentioned earlier, the matching network may be tuned to any lowertuning point, with the additional resistance making up the difference,to obtain a stable plasma. For example, in one embodiment, the matchingnetwork input impedance is tuned to about 5Ω, which results inapproximately 90% of the power “wasted” (assuming a 50Ω characteristicimpedance for the RF transmission line). As another example, tuning thematching network input impedance to about 45Ω would result inapproximately 10% of the power “wasted.” As a further example, tuningthe matching network input impedance to about 10Ω would result inapproximately 80% of the power “wasted” while tuning the matchingnetwork input impedance to about 40Ω would result in approximately 20%of the power “wasted.” Depending on the process recipe, the matchingnetwork input impedance can of course be tuned down to any desiredvalue, with the additional resistance making up the difference, toachieve a stable plasma.

Thereafter, add enough resistance (R_(X) in FIGS. 8A-8E or R_(Y) in FIG.9) to bring the input impedance of the “matching circuit” (which nowcomprises the additional resistor and the matching network) back up tothe original value of the matching network, e.g., 50Ω. This is shown instep 1608.

If desired, the length of the RF transmission line (216 or 236 in FIG.2) may be modified, in accordance with equation A6, to match the phaseof $\frac{\partial Z_{T}}{\partial P_{G}}$for the unstable plasma (with added resistor R_(X)) to the phase of$\frac{\partial Z_{T}}{\partial P_{G}}$or the stable plasma (step 1610). In some cases, however, if themagnitude of $P_{G}{\frac{\partial Z_{T}}{\partial P_{G}}}$is small enough, the system may be stable for all values of phase, inwhich case a change of the RF cable length may not be necessary.

For a particular RF generator, it is believed that the value of thecomplex quantity $P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$determine whether a given plasma will be stable or unstable. The rangesof values of $P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$that are stable or unstable depend on the characteristics of thegenerator, so that a value of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$that is unstable for a particular generator might be stable for adifferent generator.

In the past, it has been difficult lo communicate with RF generatormanufacturers the parameters or characteristics required in order tocreate an RF generator that produces stable plasmas for all processes ofinterest. One reason of this difficulty lies in the lack ofunderstanding of the underlying cause of plasma instability. In fact,many things are still not fully understood by contemporary science aboutplasma in general. Another reason relates to the fact that it isdifficult to quantify the parameters associate with RF generator designwhich affect plasma stability for processes of interest.

In accordance with one embodiment of the present invention, a techniqueis proposed to communicate and specify parameters to RF generatormanufacturers so that if those parameters are satisfied, the resultantRF generator is likely to produce stable plasmas for processes ofinterest.

For a fixed RF cable length, a particular plasma can be represented as apoint on a plot with an x-axis given by the real part of${P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}},$and y-axis given by the imaginary part of${P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}},$as shown in FIG. 17A. In accordance with one embodiment, all plasmas ofinterest (i.e., plasmas for all processes of interest) are plottedsimilarly, so that the coordinates of all the data points representingthe value of $P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$for all plasmas of interest may be obtained.

A given RF generator also has a stable operating region, and a plot forthe stable region may be measured experimentally or obtained from the RFgenerator manufacturer. An exemplary plot is shown in FIG. 17B for anexemplary RF generator. For this generator, plasmas that have values of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$within the shaded region will be stable. Plasmas that have values of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$outside of the shaded region will be unstable. In FIG. 17B, although thestable region is shown as an oval, it may in fact have any shape. In thecase of FIG. 17B, the RF generator stable operating region has a centralpart (the cross-hatched region in FIG. 17C) that is always stableregardless of the phase of$P_{G}\quad{\frac{\partial Z_{T}}{\partial P_{G}}.}$A plasma point inside this region will be stable regardless of the RFcable length. The generator stable operating region of FIG. 17B hasanother part (the cross-hatched region in FIG. 17D) that is stable forsome values of the phase of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$and not stable for other values. Finally, the generator has a region(the cross hatched area of FIG. 17E) for which all points are unstable,regardless of phase. Other RF generators may have analogous regions,albeit they may differ in shapes and sizes from those shown in FIGS.17B-17E.

By comparing the plot of FIG. 17B, representing the stable operatingregion for the RF generator and the plot of all the data pointsrepresenting the value of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$for all plasmas of interest, it is possible to predict whether the RFgenerator would produce stable plasmas for all processes of interest.

Further, the plot of all the data points representing the value of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$for all plasmas of interest can serve as a specification for agenerator. The specification would be that the generator have a stableregion, as in FIG. 17B, that encompasses all of the data pointsrepresenting the value of$P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$for all plasmas of interest. This information would then be employed bythe RF generator manufacturer to design an RF generator that wouldproduce stable plasmas for all processes of interest.

If necessary, the RF manufacturer may indicate that if the phases of thedata points are rotated by a certain amount (e.g., by changing thelength of the RF transmission line), the stable region of a furnished RFgenerator would in fact encompass the data points representing the valueof $P_{G}\quad\frac{\partial Z_{T}}{\partial P_{G}}$for all plasmas of interest (after the phase rotation). The exact valueof the phase rotation may be determined mathematically or empirically.This information would then be employed by the designer of the RF powersystem in choosing the correct length for the RF transmission line sothat stable plasmas may be achieved with the finished RF generator forall processes of interest.

Appendix A. Calculation of |DZ_(T)/DZ_(M)| for AN RF Cable to ShowEffect of RF Cable Length on the Impedance Derivatives

From Equation 1: $\begin{matrix}{Z_{T} = {R_{0}\quad\frac{Z_{M} + {{jR}_{0}{\tan\left( {2\quad\pi\quad{L/\lambda}} \right)}}}{R_{0} + {{jZ}_{M}{\tan\left( {2\quad\pi\quad{L/\lambda}} \right)}}}}} & {{Equation}\quad{A1}}\end{matrix}$

Equation A1 may be rewritten as Equation A2: $\begin{matrix}{Z_{T} = {R_{0}\quad\frac{Z_{M} + {{jR}_{0}{\tan\left( {2\quad\pi\quad{L/\lambda}} \right)}}}{R_{0} + {{jZ}_{M}{\tan\left( {2\quad\pi\quad{L/\lambda}} \right)}}}}} \\{= {{R_{0}\left( {Z_{M} + {{jR}_{0}\tan\quad\theta}} \right)}\left( {R_{0} + {{jZ}_{M}\tan\quad\theta}} \right)^{- 1}}}\end{matrix}$ where θ ≡ 2  π  L/λ

L is the length of the transmission line, and λ is the wavelength of theRF in the transmission line. $\begin{matrix}\begin{matrix}{\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}} = {{R_{0}\left( {R_{0} + {{jZ}_{M}\tan\quad\theta}} \right)}^{- 1} +}} \\{{R_{0}\left( {Z_{M} + {{jR}_{0}\tan\quad\theta}} \right)}\left( {- 1} \right)\left( {j\quad\tan\quad\theta} \right)\left( {R_{0} +} \right.} \\\left. {{jZ}_{M}\tan\quad\theta} \right)^{- 2} \\{= {\frac{R_{0}}{\left( {R_{0} + {{jZ}_{M}\tan\quad\theta}} \right)}\left\lbrack {1 - \frac{j\quad\tan\quad{\theta\left( {Z_{M} + {{jR}_{0}\tan\quad\theta}} \right)}}{\left( {R_{0} + {{jZ}_{M}\tan\quad\theta}} \right)}} \right\rbrack}} \\{= \frac{R_{0}^{2}\left( {1 + {\tan^{2}\theta}} \right)}{\left( {R_{0} + {{jZ}_{M}\tan\quad\theta}} \right)^{2}}}\end{matrix} & {{Equation}\quad{A3}}\end{matrix}$

At the tune point, Z_(M)=R₀, and $\begin{matrix}{\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}} = \frac{\left( {1 + {\tan^{2}\theta}} \right)}{\left( {1 + {j\quad\tan\quad\theta}} \right)^{2}}} & {{Equation}\quad{A4}} \\{{\frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}}} = 1} & {{Equation}\quad{A5}} \\{{{Argument}\left( \frac{\mathbb{d}Z_{T}}{\mathbb{d}Z_{M}} \right)} = {{- 2}\quad\theta}} & {{Equation}\quad{A6}}\end{matrix}$

In other words, as shown by Equation A5, the length of a losslesstransmission line does not change the magnitude of the impedancederivatives, when the terminating resistance R_(M) is equal to thetransmission line characteristic resistance R₀. The phase may be changedat the two ends of the cable (Z_(M) vs. Z_(T) across the RF cable) butthe magnitude of the change (i.e., the derivative) is the same (e.g., a1Ω change to Z_(M) results in a 1Ω increase or decrease in Z_(T) withoutchanging the magnitude of the change).

Appendix B, Calculation of L-match dZ_(M)/dZ_(S)

For the L-match network of FIG. 14 $\begin{matrix}{Z_{M} = \frac{Z_{2}Z_{3}}{Z_{2} + Z_{3}}} & {{Equation}\quad{B1}}\end{matrix}$where Z₂=jX₂ is the shunt impedance and Z₃=R_(S)+jX₃ is the sum ofseveral impedances, including the effective series plasma impedanceZ_(S). Differentiating gives: $\begin{matrix}\begin{matrix}{\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{3}} = {Z_{2}\left\lbrack {\left( {Z_{2} + Z_{3}} \right)^{- 1} - {Z_{3}\left( {Z_{2} + Z_{3}} \right)}^{- 2}} \right\rbrack}} \\{= \frac{Z_{2}^{2}}{\left( {Z_{2} + Z_{3}} \right)^{2}}} \\{= \frac{j^{2}X_{2}^{2}}{\left\lbrack {R_{S} + {j\left( {X_{2} + X_{3}} \right)}} \right\rbrack^{2}}}\end{matrix} & {{Equation}\quad{B2}}\end{matrix}$$\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{3}} = \frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}$because Z_(S) is the only part of Z₃ that varies on the time scales ofinterest (i.e., faster than the response time of the match circuit andtherefore the match capacitors can be assumed to be fixed).

The conditions for Z_(M) to be equal to R_(M) and for X_(M) to be equalto 0 are: $\begin{matrix}{{X_{3} = {\pm {{sqrt}\left( {{R_{M}R_{S}} - R_{S}^{2}} \right)}}}{X_{2} = \frac{\mu\quad R_{M}R_{S}}{{sqrt}\left( {{R_{M}R_{S}} - R_{S}^{2}} \right)}}} & {{Equation}\quad{B3}}\end{matrix}$

At the tune point, for either + or − solution: $\begin{matrix}\begin{matrix}{\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}} = \frac{\frac{{- R_{M}^{2}}R_{S}^{2}}{{R_{M}R_{S}} - R_{S}^{2}}}{\left\lbrack {R_{S} + {j\left( \frac{R_{S}^{2}}{\sqrt{{R_{M}R_{S}} - R_{S}^{2}}} \right)}} \right\rbrack^{2}}} \\{= \frac{- R_{M}^{2}}{{R_{M}R_{S}} - {2R_{S}^{2}} + {2{jR}_{S}\sqrt{{R_{M}R_{S}} - R_{S}^{2}}}}} \\{{= \frac{{- r_{S}} + {2r_{S}^{2}} + {2{jr}_{S}\sqrt{r_{S} - r_{S}^{2}}}}{\left( {r_{S} - {2r_{S}^{2}}} \right) + {4{r_{S}^{2}\left( {r_{S} - r_{S}^{2}} \right)}}}};\quad{r_{S} \equiv {R_{S}/R_{M}}}} \\{= \frac{{- r_{S}} + {2r_{S}^{2}} + {2{jr}_{S}\sqrt{r_{S} - r_{S}^{2}}}}{r_{S}^{2}}} \\{= {\frac{1}{r_{S}} + 2 + {2j\sqrt{\frac{1}{r_{S}} - 1}}}} \\{= {2 - \frac{R_{0}}{R_{S}} + {2j\sqrt{\frac{R_{M}}{R_{S}} - 1}\quad{and}}}}\end{matrix} & {{Equation}\quad{B4}} \\\begin{matrix}{{\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}} = {{sqrt}\left\lbrack {\left( {2 - \frac{R_{M}}{R_{S}} + {2j\sqrt{\frac{R_{M}}{R_{S}} - 1}}} \right)\left( {2 - \frac{R_{M}}{R_{S}} +} \right.} \right.}} \\\left. \left. {2j\sqrt{{\frac{R_{0}}{R_{S}} - 1}\quad}} \right) \right\rbrack \\{= {{sqrt}\left( {\frac{R_{M}^{2}}{R_{S}^{2}} - {4\quad\frac{R_{M}}{R_{S}}} + 4 + {4\quad\frac{R_{M}}{R_{S}}} - 4} \right)}} \\{= \frac{R_{M}}{R_{S}}}\end{matrix} & {{Equation}\quad{B5}}\end{matrix}$

Thus, the same magnification factor that the matching network applies onthe real part of the plasma impedance, R_(S), also magnifies theimpedance derivatives by the same magnification factor. Any percentagechange in R_(S) will result in the same percentage change in theimpedance derivative.

Thus, to reduce ${\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}},$one can either reduce R_(M) or increases R_(S).

Appendix C, Calculation of T-match dZ_(M)/dZ_(S)

FIG. 15 is a schematic diagram of a T-match, the impedance Z₃ includescapacitors C_(c) and C_(d), the TCP coil, and the series equivalentplasma load impedance Z_(S). $\begin{matrix}{Z_{M} = {Z_{1} + \frac{Z_{2}Z_{3}}{Z_{2} + Z_{3}}}} & {{Equation}\quad{C1}}\end{matrix}$where Z₁=jX₁ and Z₂=jX₂ are two of the match capacitors, andZ₃=R_(S)+jX₃, where R_(S) is the real part of the series equivalentplasma load impedance. Because we are interested in high-frequencyinstabilities, Z₁ can be considered to be fixed at its tune point.Differentiating gives Equation C2: $\begin{matrix}{\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{3}} = {Z_{2}\left\lbrack {\left( {Z_{2} + Z_{3}} \right)^{- 1} - {Z_{3}\left( {Z_{2} + Z_{3}} \right)}^{- 2}} \right\rbrack}} \\{= \frac{Z_{2}^{2}}{\left( {Z_{2} + Z_{3}} \right)^{2}}} \\{= \frac{j^{2}X_{2}^{2}}{\left\lbrack {R_{S} + {j\left( {X_{2} + X_{3}} \right)}} \right\rbrack^{2}}}\end{matrix}$$\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{3}} = \frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}$because Z_(S) is the only part of Z₃ that varies on the time scales ofinterest.

The conditions for Z_(M) to be equal to R_(M) and for X_(M) to be equalto 0 are: $\begin{matrix}{{X_{3} = {{- X_{2}} \pm \sqrt{\frac{X_{2}^{2}R_{S}}{R_{M}} - R_{S}^{2}}}}{X_{1} = {{- X_{2}} \pm \sqrt{\frac{X_{2}^{2}R_{M}}{R_{S}} - R_{M}^{2}}}}} & {{Equation}\quad{C3}}\end{matrix}$

Substituting the above value of X₃ into equation C2 gives the derivativeof the match input impedance with respect to the series equivalentplasma load impedance when Z_(M)=R_(M) and X_(M)=0: $\begin{matrix}\begin{matrix}{\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}} = \frac{- X_{2}^{2}}{{R_{S}^{2} \pm {2{jR}_{S}\sqrt{\frac{X_{2}^{2}R_{S}}{R_{M}} - R_{S}^{2}}}} - \left( {\frac{X_{2}^{2}R_{S}}{R_{M}} - R_{S}^{2}} \right)}} \\{= \frac{- X_{2}^{2}}{{2R_{S}^{2}} - {\frac{X_{2}^{2}R_{S}}{R_{M}} \pm {2{jR}_{S}\sqrt{\frac{X_{2}^{2}R_{S}}{R_{M}} - R_{S}^{2}}}}}} \\{= \frac{- {X_{2}^{2}\left( {{2R_{S}^{2}} - {\frac{X_{2}^{2}R_{S}}{R_{M}}\mu\quad 2{jR}_{S}\sqrt{\frac{X_{2}^{2}R_{S}}{R_{M}} - R_{S}^{2}}}} \right)}}{\left( {{2R_{S}^{2}} - \frac{X_{2}^{2}R_{S}}{R_{M}}} \right)^{2} + {4{R_{S}^{2}\left( {\frac{X_{2}^{2}R_{S}}{R_{M}} - R_{S}^{2}} \right)}}}} \\{= {\frac{- R_{0}^{2}}{X_{2}^{2}R_{S}^{2}}\left( {{2R_{S}^{2}} - {\frac{X_{2}^{2}R_{S}}{R_{M}}\mu\quad 2{jR}_{S}\sqrt{\frac{X_{2}^{2}R_{S}}{R_{M}} - R_{S}^{2}}}} \right)}} \\{= {\frac{{- 2}R_{M}^{2}}{X_{2}^{2}} + {\frac{R_{M}}{R_{S}} \pm {2j\quad\frac{R_{M}^{2}}{X_{2}^{2}}\sqrt{\frac{X_{2}^{2}}{R_{M}R_{S}} - 1}}}}}\end{matrix} & {{Equation}\quad{C4}} \\\begin{matrix}{{\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}}^{2} = {\frac{4R_{M}^{4}}{X_{2}^{4}} - {\frac{4R_{M}^{2}}{X_{2}^{2}}\quad\frac{R_{M}}{R_{S}}} + \frac{R_{M}^{2}}{R_{S}^{2}} +}} \\{\frac{4R_{M}^{4}}{X_{2}^{4}}\left( {\frac{X_{2}^{2}}{R_{M}R_{S}} - 1} \right)} \\{= \frac{R_{M}^{2}}{R_{S}^{2}}}\end{matrix} & {{Equation}\quad{C5}} \\{{\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}} = \frac{R_{M}}{R_{S}}} & {{Equation}\quad{C6}}\end{matrix}$

This is the same result as for the L-match, equation B5. Again, the samemagnification factor that the matching network applies on the real partof the plasma impedance, R_(S), also magnifies the impedance derivativesby the same magnification factor. Again, to reduce${\frac{\mathbb{d}Z_{M}}{\mathbb{d}Z_{S}}},$one can either reduce R_(M) or increases R_(S).

It should be noted that the same result is also obtained for the Π-matchnetwork For brevity's sake, the arithmetic is not repeated here.

Thus, while this invention has been described in terms of severalpreferred embodiments, there are alterations, permutations, andequivalents which fall within the scope of this invention. For example,although the impedance elements in the match networks are shown to becapacitors, it should be understood that such impedance elements mayalso be implemented by inductors and/or a combination of inductors andcapacitor (both fixed and variable). As a further example, a separateterminating capacitor C_(d) (such as that shown in FIG. 9) may not berequired on all chamber configurations.

As yet another example, although the top RF electrode has been discussedas the RF electrode in the exemplary RF power system, it should beunderstood that the invention also applies when the electrode isprimarily capacitive, such as a bias electrode or an electrode in acapacitively coupled plasma system. Furthermore, some components may beoptional and other optional and/or conventional components may beomitted from the figures. As the components are shown, indicated, ormentioned as being coupled together, it should be understood that thesecomponents may in some cases be physically connected, and in othercases, may simply be in the same current path, with one or morecomponents disposed in between.

Furthermore, although the exemplary RF power arrangements discussedherein are disclosed to have an RF transmission line, such RFtransmission line is not absolutely required to practice the invention.For example, some integrated RF power arrangements may not require theuse of an RF transmission line to couple the matching network to the RFgenerator. Instead, these integrated RF power arrangements may directlycouple the RF generator output to the matching network, and in somecases, the matching network directly connected to the RF load (such asthe RF antenna or RF electrode). Irrespective whether the RFtransmission cable is present, the use of the additional resistanceand/or power attenuator to reduce the load impedance with respect topower and to achieve improved plasma stability would still apply.Additionally, it is also possible to employ the present invention tocommunicate the plama stability requirement to the manufacturer of suchintegrated RF power arrangements and to furnish the manufacturer with anefficient way to determine whether a particular RF generator and/ormatching network would satisfy the requirement with respect to plasmastability.

It should also be noted that there are many alternative ways ofimplementing the methods and apparatuses of the present invention. It istherefore intended that the following appended claims be interpreted asincluding all such alterations, permutations, and equivalents as fallwithin the true spirit and scope of the present inventions.

1. A plasma processing system for processing semiconductor substrates,comprising: an RF generator having an RF generator output; an RFtransmission line coupled to said RF generator output, said RFtransmission line having a characteristic impedance; and a matchingcircuit coupled to said RF transmission line, said matching circuithaving a first resistor and a matching network, said matching networkhaving a plurality of impedance devices, wherein said first resistor iscoupled to at least one terminal of one of said plurality of impedancedevices, and wherein an input impedance of said matching circuit issubstantially equal to said characteristic impedance of said RFtransmission line.
 2. The plasma processing system of claim 1 whereinsaid first resistor is a discrete resistor.
 3. The plasma processingsystem of claim 1 wherein said first resistor is inherently implementedby a low conductance material in one of an inductive element in saidmatching network and a connector in said plasma processing system. 4.The plasma processing system of claim 3 wherein low conductance materialis one of stainless steel, nichrome, chromel, graphite, and SiC.
 5. Theplasma processing system of claim 1 wherein said matching network is aπ-match network.
 6. The plasma processing system of claim 5 wherein saidπ-match network has a first T-junction and a second T-junction, saidfirst T-junction being coupled to a first impedance device and a secondimpedance device of said plurality of impedance devices and to an inputterminal of said π-match network, said second T-junction being coupledto a third impedance device and said second impedance device of saidplurality of impedance devices and to an output terminal of said π-matchnetwork, said first impedance device and said third impedance devicealso being coupled to ground, said second device being coupled in seriesbetween said first T-junction and said second T-junction, said firstresistor being coupled in series between said second T-junction and saidthird impedance device.
 7. The plasma processing system of claim 5wherein said π-match network has a first T-junction and a secondT-junction, said first T-junction being coupled to a first impedancedevice and a second impedance device of said plurality of impedancedevices and to an input terminal of said π-match network, said secondT-junction being coupled to a third impedance device and said secondimpedance device of said plurality of impedance devices and to an outputterminal of said π-match network, said first impedance device and saidthird impedance device also being coupled to ground, said second devicebeing coupled in series between said first T-junction and said secondT-junction, said first resistor being coupled in series between saidthird impedance device and said ground.
 8. The plasma processing systemof claim 5 wherein said π-match network has a first T-junction and asecond T-junction, said first T-junction being coupled to a firstimpedance device and a second impedance device of said plurality ofimpedance devices and to an input terminal of said π-match network, saidsecond T-junction being coupled to a third impedance device and saidsecond impedance device of said plurality of impedance devices and to anoutput terminal of said π-match network, said first impedance device andsaid third impedance device also being coupled to ground, said seconddevice being coupled in series between said first T-junction and saidsecond T-junction, said first resistor being coupled in series betweensaid second impedance device and said second T-junction.
 9. The plasmaprocessing system of claim 5 wherein said π-match network has a firstT-junction and a second T-junction, said first T-junction being coupledto a first impedance device and a second impedance device of saidplurality of impedance devices and to an input terminal of said π-matchnetwork, said second T-junction being coupled to a third impedancedevice and said second impedance device of said plurality of impedancedevices and to an output terminal of said π-match network, said firstimpedance device and said third impedance device also being coupled toground, said second device being coupled in series between said firstT-junction and said second T-junction, said first resistor being coupledin series between said second impedance device and said firstT-junction.
 10. The plasma processing system of claim 5 wherein saidπ-match network has a first T-junction and a second T-junction, saidfirst T-junction being coupled to a first impedance device and a secondimpedance device of said plurality of impedance devices and to an inputterminal of said π-match network, said second T-junction being coupledto a third impedance device and said second impedance device of saidplurality of impedance devices and to an output terminal of said π-matchnetwork, said first impedance device and said third impedance devicealso being coupled to ground, said second device being coupled in seriesbetween said first T-junction and said second T-junction, said firstresistor being coupled in series between said first impedance device andsaid first T-junction.
 11. The plasma processing system of claim 5wherein said π-match network has a first T-junction and a secondT-junction, said first T-junction being coupled to a first impedancedevice and a second impedance device of said plurality of impedancedevices and to an input terminal of said π-match network, said secondT-junction being coupled to a third impedance device and said secondimpedance device of said plurality of impedance devices and to an outputterminal of said π-match network, said first impedance device and saidthird impedance device also being coupled to ground, said second devicebeing coupled in series between said first T-junction and said secondT-junction, said first resistor being coupled in series between saidfirst impedance device and said ground.
 12. The plasma processing systemof claim 1 wherein said matching network is a T-match network.
 13. Theplasma processing system of claim 12 wherein said T-match network has afirst T-junction, a first impedance device of said plurality ofimpedance devices being coupled between said first T-junction and aninput terminal of said T-match network, a second impedance device ofsaid plurality of impedance devices being coupled between said firstT-junction and ground, a third impedance device of said plurality ofimpedance devices being coupled between said first T-junction and anoutput terminal of said T-match network, said first resistor beingcoupled between said first impedance device and said first T-junction.14. The plasma processing system of claim 12 wherein said T-matchnetwork has a first T-junction, a first impedance device of saidplurality of impedance devices being coupled between said firstT-junction and an input terminal of said T-match network, a secondimpedance device of said plurality of impedance devices being coupledbetween said first T-junction and ground, a third impedance device ofsaid plurality of impedance devices being coupled between said firstT-junction and an output terminal of said T-match network, said firstresistor being coupled between said first T-junction and said secondimpedance device.
 15. The plasma processing system of claim 12 whereinsaid T-match network has a first T-junction, a first impedance device ofsaid plurality of impedance devices being coupled between said firstT-junction and an input terminal of said T-match network, a secondimpedance device of said plurality of impedance devices being coupledbetween said first T-junction and ground, a third impedance device ofsaid plurality of impedance devices being coupled between said firstT-junction and an output terminal of said T-match network, said firstresistor being coupled between said second impedance device and ground.16. The plasma processing system of claim 1 wherein at least one of saidplurality of impedance devices is a capacitor.
 17. The plasma processingsystem of claim 1 wherein at least one of said plurality of impedancedevices is an inductor.
 18. The plasma processing system of claim 1wherein said first resistor is fixed.
 19. The plasma processing systemof claim 1 wherein said first resistor is variable.
 20. The plasmaprocessing system of claim 1 wherein said first resistor is switched, aresistance value across an input terminal of said resistor and an outputterminal of said resistor having a first value when in a first state,said resistance value across said input terminal and said outputterminal of said first resistor having a second value when in a secondstate.
 21. The plasma processing system of claim 20 wherein said firstvalue is substantially zero.
 22. The plasma processing system of claim 1wherein said first resistor is liquid-cooled.
 23. The plasma processingsystem of claim 1 further comprising a chamber, said chamber beingconfigured to generate inductively-coupled plasma.
 24. The plasmaprocessing system of claim 1 further comprising a chamber, said chamberbeing configured to generate capacitively-coupled plasma.
 25. The plasmaprocessing system of claim 1 wherein said first resistor is in serieswith an input of said matching network, an input impedance of saidmatching network is lower than said characteristic impedance of said RFtransmission line.
 26. The plasma processing system of claim 25 whereinsaid matching network is a T-match network.
 27. The plasma processingsystem of claim 26 wherein said first resistor is coupled in seriesbetween said RF transmission line and an input terminal of said T-matchnetwork.
 28. The plasma processing system of claim 26 wherein saidT-match network has a first T-junction, a first impedance device of saidplurality of impedance devices being coupled between said firstT-junction and an input terminal of said T-match network, a secondimpedance device of said plurality of impedance devices having twoterminals, a first one of said two terminals of said second impedancedevice being coupled to said first T-junction, a third impedance of saidplurality of impedance being coupled between said first T-junction andan output terminal of said T-match network, said first resistor having afirst resistor terminal and a second resistor terminal, said firstresistor terminal being coupled to a second one of said two terminals ofsaid second impedance device, said second resistor terminal beingcoupled to ground.
 29. The plasma processing system of claim 24 whereinsaid first resistor is a discrete resistor.
 30. The plasma processingsystem of claim 26 wherein said first resistor is inherently implementedby a low conductance material in one of an inductive element in saidmatching network and a connector in said plasma processing system. 31.The plasma processing system of claim 30 wherein low conductancematerial is one of stainless steel, nichrome, chromel, graphite, andSiC.
 32. The plasma processing system of claim 26 wherein at least oneof said plurality of impedance devices is a capacitor.
 33. The plasmaprocessing system of claim 26 wherein at least one of said plurality ofimpedance devices is an inductor.
 34. The plasma processing system of 26wherein said a resistance value of said first resistor is between 10%and 90% of an impedance value of said input impedance of said matchingcircuit.
 35. The plasma processing system of 26 wherein said aresistance value of said first resistor is between 20% and 80% of animpedance value of said input impedance of said matching circuit. 36.The plasma processing system of claim 26 wherein said first resistor isfixed.
 37. The plasma processing system of claim 26 wherein said firstresistor is variable.
 38. The plasma processing system of claim 26wherein said first resistor is switched, a resistance value across aninput terminal of said resistor and an output terminal of said resistorhaving a first value when in a first state, said resistance value acrosssaid input terminal and said output terminal of said first resistorhaving a second value when in a second state.
 39. The plasma processingsystem of claim 26 wherein said first value is substantially zero. 40.The plasma processing system of claim 26 wherein said first resistor isliquid-cooled.
 41. The plasma processing system of claim 26 furthercomprising a chamber, said chamber being configured to generateinductively-coupled plasma.
 42. The plasma processing system of claim 26further comprising a chamber, said chamber being configured to generatecapacitively-coupled plasma.
 43. The plasma processing system of claim25 wherein said matching network is an L-match network.
 44. The plasmaprocessing system of claim 43 wherein first resistor is coupled betweensaid RF transmission line and an input terminal of said L-match network.45. The plasma processing system of claim 43 wherein said L-matchnetwork has a first impedance device having two terminals, a first oneof said two terminals of said first impedance device being coupled to aninput terminal of said L-match network, said second impedance devicebeing coupled between said input terminal of said L-match network and aload, said first resistor being coupled between a second one of said twoterminals of said first impedance device and ground.
 46. The plasmaprocessing system of claim 43 wherein said first resistor is inherentlyimplemented by a low conductance material in one of an inductive elementin said matching network and a connector in said plasma processingsystem.
 47. The plasma processing system of claim 46 wherein lowconductance material is one of stainless steel, nichrome, chromel,graphite, and SiC.
 48. The plasma processing system of claim 43 whereinat least one of said plurality of impedance devices is a capacitor. 49.The plasma processing system of claim 43 wherein at least one of saidplurality of impedance devices is an inductor.
 50. The plasma processingsystem of 43 wherein said a resistance value of said first resistor isbetween 10% and 90% of an impedance value of said input impedance ofsaid matching circuit.
 51. The plasma processing system of 43 whereinsaid a resistance value of said first resistor is between 20% and 80% ofan impedance value of said input impedance of said matching circuit. 52.The plasma processing system of claim 43 wherein said first resistor isfixed.
 53. The plasma processing system of claim 43 wherein said firstresistor is variable.
 54. The plasma processing system of claim 43wherein said first resistor is switched, a resistance value across aninput terminal of said resistor and an output terminal of said resistorhaving a first value when in a first state, said resistance value acrosssaid input terminal and said output terminal of said first resistorhaving a second value when in a second state.
 55. The plasma processingsystem of claim 54 wherein said first value is substantially zero. 56.The plasma processing system of claim 43 wherein said first resistor isliquid-cooled.
 57. The plasma processing system of claim 43 furthercomprising a chamber, said chamber being configured to generateinductively-coupled plasma.
 58. The plasma processing system of claim 43further comprising a chamber, said chamber being configured to generatecapacitively-coupled plasma.
 59. The plasma processing system of claim43 wherein said first resistor is in series with an input of saidmatching network, an input impedance of said matching network is lowerthan said characteristic impedance of said RF transmission line, saidmatching network is an L-match network, and said first resistor is adiscrete resistor.
 60. The plasma processing system of claim 25 whereinsaid matching network is a π-match network.
 61. The plasma processingsystem of claim 60 wherein said first resistor is coupled in seriesbetween said RF transmission line and an input terminal of said π-matchnetwork.
 62. The plasma processing system of claim 60 wherein said firstresistor is a discrete resistor.
 63. The plasma processing system ofclaim 60 wherein said first resistor is inherently implemented by a lowconductance material in one of an inductive element in said matchingnetwork and a connector in said plasma processing system.
 64. The plasmaprocessing system of claim 63 wherein low conductance material is one ofstainless steel, nichrome, chromel, graphite, and SiC.
 65. The plasmaprocessing system of claim 60 wherein at least one of said plurality ofimpedance devices is a capacitor.
 66. The plasma processing system ofclaim 60 wherein at least one of said plurality of impedance devices isan inductor.
 67. The plasma processing system of 60 wherein said aresistance value of said first resistor is between 10% and 90% of animpedance value of said input impedance of said matching circuit. 68.The plasma processing system of 60 wherein said a resistance value ofsaid first resistor is between 20% and 80% of an impedance value of saidinput impedance of said matching circuit.
 69. The plasma processingsystem of claim 60 wherein said first resistor is fixed.
 70. The plasmaprocessing system of claim 60 wherein said first resistor is variable.71. The plasma processing system of claim 60 wherein said first resistoris switched, a resistance value across an input terminal of saidresistor and an output terminal of said resistor having a first valuewhen in a first state, said resistance value across said input terminaland said output terminal of said first resistor having a second valuewhen in a second state.
 72. The plasma processing system of claim 71wherein said first value is substantially zero.
 73. The plasmaprocessing system of claim 60 wherein said first resistor isliquid-cooled.
 74. The plasma processing system of claim 60 furthercomprising a chamber, said chamber being configured to generateinductively-coupled plasma.
 75. The plasma processing system of claim 60further comprising a chamber, said chamber being configured to generatecapacitively-coupled plasma.
 76. The plasma processing system of claim 1wherein said first resistor is in series with an equivalent plasmaimpedance that exists during said processing.
 77. The plasma processingsystem of claim 76 wherein said first resistor is coupled in seriesbetween an output of said matching network and said equivalent plasmaimpedance.
 78. The plasma processing system of claim 76 wherein saidfirst resistor is inherently implemented by a low conductance materialin one of an inductive clement in said matching network and a connectorin said plasma processing system.
 79. The plasma processing system ofclaim 76 wherein said first resistor is coupled in series between an RFantenna inductance L_(A) and a terminating capacitor C_(d).
 80. Theplasma processing system of claim 76 wherein said first resistor iscoupled in series between a terminating capacitor C_(d) and ground. 81.The plasma processing system of claim 76 wherein said matching networkis a T-match network.
 82. The plasma processing system of claim 81wherein said first resistor disposed in series between a terminatingcapacitor C_(d) and ground.
 83. The plasma processing system of claim 81wherein said first resistor is disposed in one of a first position and asecond position, said first position is disposed in series between anoutput of said matching network and said equivalent plasma impedance,said second position is disposed in series between an RF antennainductance L_(A) and a terminating capacitor C_(d).
 84. The plasmaprocessing system of claim 81 wherein said first resistor is a discreteresistor.
 85. The plasma processing system of claim 81 wherein saidfirst resistor is inherently implemented by a low conductance materialin one of an inductive element in said matching network and a connectorin said plasma processing system.
 86. The plasma processing system ofclaim 85 wherein low conductance material is one of stainless steel,nichrome, chromel, graphite, and SiC.
 87. The plasma processing systemof claim 81 wherein at least one of said plurality of impedance devicesis a capacitor.
 88. The plasma processing system of claim 81 wherein atleast one of said plurality of impedance devices is an inductor.
 89. Theplasma processing system of 81 wherein said a resistance value of saidfirst resistor is between about 10% and about 90% of a resistance sumvalue, said resistance sum value equals said resistance value of saidfirst resistor plus a series equivalent plasma load resistance in aplasma processing chamber of said plasma processing system duringprocessing.
 90. The plasma processing system of 81 wherein said aresistance value of said first resistor is between 20% and 80% of aresistance sum value, said resistance sum value equals said resistancevalue of said first resistor plus a series equivalent plasma loadresistance in a plasma processing chamber of said plasma processingsystem during processing.
 91. The plasma processing system of claim 81wherein said first resistor is fixed.
 92. The plasma processing systemof claim 81 wherein said first resistor is variable.
 93. The plasmaprocessing system of claim 92 wherein said first resistor is switched, aresistance value across an input terminal of said resistor and an outputterminal of said resistor having a first value when in a first state,said resistance value across said input terminal and said outputterminal of said first resistor having a second value when in a secondstate.
 94. The plasma processing system of claim 93 wherein said firstvalue is substantially zero.
 95. The plasma processing system of claim92 wherein said first resistor is switched, a resistance value across aninput terminal of said resistor and an output terminal of said resistorhaving a first value when in a first state, said resistance value acrosssaid input terminal and said output terminal of said first resistorhaving a second value when in a second state.
 96. The plasma processingsystem of claim 92 wherein said first resistor is switched, a resistancevalue across an input terminal of said resistor and an output terminalof said resistor having a first value when in a first state, saidresistance value across said input terminal and said output terminal ofsaid first resistor having a second value when in a second state. 97.The plasma processing system of claim 81 wherein said first resistor isliquid-cooled.
 98. The plasma processing system of claim 81 furthercomprising a chamber, said chamber being configured to generateinductively-coupled plasma.
 99. The plasma processing system of claim 81further comprising a chamber, said chamber being configured to generatecapacitively-coupled plasma.
 100. The plasma processing system of claim76 wherein said matching network is an L-match network.
 101. The plasmaprocessing system of claim 100 wherein said first resistor is coupled toa first impedance device of said L-match network, a second impedancedevice of said L-match, and an input of said L-match network.
 102. Theplasma processing system of claim 100 wherein said first resistor isdisposed in one of a first position, a second position, and a thirdposition, said first position is disposed in series between an output ofsaid L-match network and said equivalent plasma impedance, said secondposition is disposed in series between an RF antenna inductance L_(A)and a terminating capacitor C_(d), said third position is disposed inseries between said terminating capacitor C_(d) and ground.
 103. Theplasma processing system of claim 100 wherein said first resistor is adiscrete resistor.
 104. The plasma processing system of claim 100wherein said first resistor is inherently implemented by a lowconductance material in one of an inductive element in said matchingnetwork and a connector in said plasma processing system.
 105. Theplasma processing system of claim 104 wherein low conductance materialis one of stainless steel, nichrome, chromel, graphite, and SiC. 106.The plasma processing system of claim 104 wherein low conductancematerial is one of stainless steel, nichrome, chromel, graphite, andSiC.
 107. The plasma processing system of claim 100 wherein at least oneof said plurality of impedance devices is a capacitor.
 108. The plasmaprocessing system of claim 100 wherein at least one of said plurality ofimpedance devices is an inductor.
 109. The plasma processing system of100 wherein said a resistance value of said first resistor is betweenabout 10% and about 90% of a resistance sum value, said resistance sumvalue equals said resistance value of said first resistor plus a seriesequivalent plasma load resistance in a plasma processing chamber of saidplasma processing system during processing.
 110. The plasma processingsystem of 100 wherein said a resistance value of said first resistor isbetween 20% and 80% of a resistance sum value, said resistance sum valueequals said resistance value of said first resistor plus a seriesequivalent plasma load resistance in a plasma processing chamber of saidplasma processing system during processing.
 111. The plasma processingsystem of claim 100 wherein said first resistor is fixed.
 112. Theplasma processing system of claim 100 wherein said first resistor isvariable.
 113. The plasma processing system of claim 100 wherein saidfirst value is substantially zero.
 114. The plasma processing system ofclaim 95 wherein said first resistor is liquid-cooled.
 115. The plasmaprocessing system of claim 100 further comprising a chamber, saidchamber being configured to generate inductively-coupled plasma. 116.The plasma processing system of claim 100 farther comprising a chamber,said chamber being configured to generate capacitively-coupled plasma.117. The plasma processing system of claim 76 wherein said matchingnetwork is an π-match network.
 118. The plasma processing system ofclaim 117 wherein said first resistor is disposed in series between aterminating capacitor C_(d) and ground.
 119. The plasma processingsystem of claim 117 wherein said first resistor is disposed in one of afirst position, and a second position, said first position is disposedin series between an output of said π-match network and said equivalentplasma impedance, said second position is disposed in series between anRF antenna inductance L_(A) and a terminating capacitor C_(d).
 120. Theplasma processing system of claim 117 wherein said first resistor is adiscrete resistor.
 121. The plasma processing system of claim 117wherein said first resistor is inherently implemented by a lowconductance material in one of an inductive element in said matchingnetwork and a connector in said plasma processing system.
 122. Theplasma processing system of claim 121 wherein at least one of saidplurality of impedance devices is a capacitor.
 123. The plasmaprocessing system of claim 117 wherein at least one of said plurality ofimpedance devices is an inductor.
 124. The plasma processing system of117 wherein said a resistance value of said first resistor is betweenabout 10% and about 90% of a resistance sum value, said resistance sumvalue equals said resistance value of said first resistor plus a seriesequivalent plasma load resistance in a plasma processing chamber of saidplasma processing system during processing.
 125. The plasma processingsystem of 117 wherein said a resistance value of said first resistor isbetween 20% and 80% of a resistance sum value, said resistance sum valueequals said resistance value of said first resistor plus a seriesequivalent plasma load resistance in a plasma processing chamber of saidplasma processing system during processing.
 126. The plasma processingsystem of claim 117 wherein said first resistor is fixed.
 127. Theplasma processing system of claim 117 wherein said first resistor isvariable.
 128. The plasma processing system of claim 117 wherein saidfirst value is substantially zero.
 129. The plasma processing system ofclaim 117 wherein said first resistor is liquid-cooled.
 130. The plasmaprocessing system of claim 117 further comprising a chamber, saidchamber being configured to generate inductively-coupled plasma. 131.The plasma processing system of claim 117 further comprising a chamber,said chamber being configured to generate capacitively-coupled plasma.132. The plasma processing system of claim 1 wherein said first resistoris in series with an equivalent plasma impedance that exists during saidprocessing, said matching network is a T-match network having a firstT-junction, a first impedance device of said plurality of impedancedevices being coupled between said first T-junction and an inputterminal of said T-match network, a second impedance device of saidplurality of impedance devices being coupled between said firstT-junction and ground, a third impedance of said plurality of impedancebeing coupled between said first T-junction and an output terminal ofsaid T-match network, said first resistor being coupled in seriesbetween said first T-junction and said third impedance device.
 133. Theplasma processing system of claim 1 wherein said L-match network has afirst impedance device and a second impedance device, said firstimpedance device having two terminals, a first one of said two terminalsof said first impedance device being coupled to ground, said secondimpedance device being coupled between said input terminal of saidL-match network and a load, said first resistor having a first resistorterminal and a second resistor terminal, said first resistor terminalbeing coupled to a second one of said two terminals of said firstimpedance device, said second resistor terminal being coupled to saidinput terminal of said L-match network.
 134. The plasma processingsystem of claim 1 wherein said L-match network has a first impedancedevice and a second impedance device, said first impedance device havingtwo terminals, a first one of said two terminals of said first impedancedevice being coupled to an input terminal of said L-match network, saidsecond impedance device being coupled between said input terminal ofsaid L-match network and a load, said first resistor having a firstresistor terminal and a second resistor terminal, said first resistorterminal being coupled to a second one of said two terminals of saidfirst impedance device, said second resistor terminal being coupled toground.
 135. The plasma processing system of claim 43 wherein said firstresistor is in series with an input of said matching network, an inputimpedance of said matching network is lower than said characteristicimpedance of said RF transmission line, said matching network is anL-match network, and said first resistor is a discrete resistor. 136.The plasma processing system of claim 135 wherein said RF powerattenuator comprises resistors arranged in a T configuration.
 137. Theplasma processing system of claim 135 wherein said RF power attenuatorcomprises resistors arranged in a π configuration.
 138. The plasmaprocessing system of claim 135 wherein said RF power attenuator is oneof an L attenuator, an H attenuator, an O attenuator, a bridged Tattenuator, and a bridged H attenuator.
 139. The plasma processingsystem of 135 wherein said RF power attenuator attenuates between 10%and 90% of RF power outputted by said RF generator.
 140. The plasmaprocessing system of 135 wherein said RF power attenuator attenuatesbetween 20% and 80% of RF power outputted by said RF generator.
 141. Theplasma processing system of claim 135 wherein said RF power attenuatoris disposed between said first RF transmission line and said matchingnetwork.
 142. The plasma processing system of claim 141 wherein saidmatching network is coupled to said RF power attenuator.
 143. The plasmaprocessing system of claim 141 wherein said first RF transmission lineis coupled to said RF generator.
 144. The plasma processing system ofclaim 143 further comprising a second RF transmission line having afirst end and a second end, said first end being coupled to saidmatching network, said second end being coupled with a terminal of saidRF power attenuator, another terminal of said RF power attenuator beingcoupled to said first RF transmission line.
 145. The plasma processingsystem of claim 135 wherein said first RF power attenuator is disposedbetween said RF generator and said RF transmission line, said first RFtransmission line being coupled to said matching network.
 146. Theplasma processing system of claim 135 further comprising a chamber,wherein the RF power is inductively coupled to a plasma within saidchamber.
 147. The plasma processing system of claim 135 furthercomprising a chamber, wherein the RF power is capacitively coupled to aplasma within said chamber.
 148. A method for configuring a plasmaprocessing system, said plasma processing system being configured forprocessing semiconductor substrates, comprising: providing an RF powerarrangement including an RF generator having an RF generator output, afirst RF transmission line coupled to receive RF current from said RFgenerator output during operation, said first RF transmission linehaving a characteristic impedance, a matching network having an inputimpedance substantially equal to said characteristic impedance of saidfirst RF transmission line, said matching network being configured toreceive said RF current from said RF generator through said first RFtransmission line; and coupling an RF power attenuator in a current pathbetween said RF generator and said matching network.
 149. The method ofclaim 148 wherein said RF power attenuator comprises resistors arrangedin a T configuration.
 150. The method of claim 148 wherein said RF powerattenuator comprises resistors arranged in a π configuration.
 151. Themethod of claim 148 wherein said RF power attenuator is one of an Lattenuator, an H attenuator, an O attenuator, a bridged T attenuator,and a bridged H attenuator.
 152. The method of 148 wherein said RF powerattenuator attenuates between 10% and 90% of RF power outputted by saidRF generator.
 153. The method of 148 wherein said RF power attenuatorattenuates between 20% and 80% of RF power outputted by said RFgenerator.
 154. The method of claim 148 wherein said RF power attenuatoris disposed between said first RF transmission line and said matchingnetwork.
 155. The method of claim 154 wherein said matching network iscoupled to said RF power attenuator.
 156. The method of claim 154wherein said first RF transmission line is coupled to said RF generator.157. The method of claim 156 wherein said RF power arrangement furthercomprising a second RF transmission line having a first end and a secondend, said first end being coupled to said matching network, said secondend being coupled with a terminal of said RF power attenuator, anotherterminal of said RF power attenuator being coupled to said first RFtransmission line.
 158. The method of claim 148 wherein said first RFpower attenuator is disposed between said RF generator and said first RFtransmission line, said first RF transmission line being coupled to saidmatching network.
 159. The method of claim 148 further comprising achamber, wherein the RF power is inductively coupled to a plasma withinsaid chamber.
 160. The method of claim 148 further comprising a chamber,wherein the RF power is capacitively coupled to a plasma within saidchamber.
 161. A plasma processing system, comprising: an RF generatorhaving an RF generator output; a first RF transmission line coupled toreceive RF current from said RF generator output, said RF transmissionline having a characteristic impedance; a matching network having aninput impedance substantially equal to said characteristic impedance ofsaid RF transmission line, said matching network being configured toreceive said RF current from said RF generator through said RFtransmission line, wherein both said input impedance of said matchingnetwork and said characteristic impedance of said RE transmission lineare substantially equal to a given value, said given value beingdesigned to be lower than 50 Ω, said RF generator being configured todeliver RF power into a load having said given value.
 162. The plasmaprocessing system of claim 161 wherein said given value is between about5 Ω and about 45Ω.
 163. The plasma processing system of claim 161wherein said given value is between about 10 Ω and about 40Ω.
 164. Theplasma processing system of claim 161 further comprising a chamber, saidchamber being configured to generate inductively-coupled plasma. 165.The plasma processing system of claim 161 further comprising a chamber,said chamber being configured to generate capacitively-coupled plasma.166. The plasma processing system of claim 161 wherein said given valueis about 25Ω.
 167. The plasma processing system of claim 166 whereinsaid RF transmission comprises two 50 Ω transmission lines in parallel.168. A method for configuring a plasma processing system, said plasmaprocessing system being configured for processing semiconductorsubstrates, comprising: providing an RF generator having an RF generatoroutput; configuring a first RF transmission line to receive RF currentfrom said RF generator output, said RF transmission line having acharacteristic impedance; providing a matching network having an inputimpedance substantially equal to said characteristic impedance of saidRF transmission line, said matching network being configured to receivesaid RF current from said RF generator through said RF transmissionline, wherein both said input impedance of said matching network andsaid characteristic impedance of said RF transmission line aresubstantially equal to a given value, said given value being designed tobe lower than 50 Ω said RF generator being configured to deliver RFpower into a load having said given value.
 169. The method of claim 168wherein said given value is between about 5 Ω and about 45Ω.
 170. Themethod of claim 168 wherein said given value is between about 10 Ω andabout 40Ω.
 171. The method of claim 168 wherein said plasma processingsystem includes a chamber, said chamber being configured to generateinductively-coupled plasma.
 172. The method of claim 168 wherein saidplasma processing system includes a chamber, said chamber beingconfigured to generate capacitively-coupled plasma.
 173. The method ofclaim 168 wherein said given value is about 25Ω.
 174. The method ofclaim 173 wherein said RF transmission comprises two 50 Ω transmissionlines in parallel.